# At one school, the mean amount of t - Expert Answers

Question 1 of 40
At one school, the mean amount of time that tenth-graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.
Formulate the null and alternative hypotheses for the study described.
A.
Ho: µ = 18.4 hours H  : µ  18.4 hours
B.
Ho: µ = 18.4 hours H  : µ < 18.4 hours
C.
Ho: µ  18.4 hours H  : µ < 18.4 hours
D.
Ho: µ = 18.4 hours H  : µ 18.4 hours
Question 3 of 40
The owner of a football team claims that the average attendance at home games is over 3000, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in non-technical terms.
A. There is sufficient evidence to support the claim that the mean attendance is greater than 3000.
B. There is sufficient evidence to support the claim that the mean attendance is equal to 3000.
C. There is not sufficient evidence to support the claim that the mean attendance is greater than 3000.
D. There is not sufficient evidence to support the claim that the mean attendance is less than 3000.
Question 6 of 40
In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. The mean duration for a random sample of 50 calls originating in the town was 8.6 minutes. Does the data provide sufficient evidence to conclude that the mean call duration, µ, is different from the 1990 mean of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of 0.01. Assume that = 4.8 minutes.
A. With a z of -1.2 there is sufficient evidence to conclude that the mean
value has changed from the 1990 mean of 9.4 minutes.
B. With a P-value of 0.2302 there is not sufficient evidence to conclude
that the mean value is less than the 1990 mean of 9.4 minutes.
C. With a P-value of 0.2302 there is sufficient evidence to conclude that
the mean value is less than the 1990 mean of 9.4 minutes.
D. With a z of –1.2 there is not sufficient evidence to conclude that the
mean value has changed from the 1990 mean of 9.4 minutes.
Question 7 of 40
A supplier of DVDs claims that no more than 1% of the DVDs are defective. In a random sample of 600 DVDs, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplier’s claim that no more than 1% are defective.
A. Do not reject the null hypothesis and conclude that there is evidence to support the claim that more than 1% of the DVDs are defective.
B. Reject the null hypothesis and conclude that there is insufficient evidence to support the claim that more than 1% of the DVDs are defective.
C. Do not reject the null hypothesis and conclude that there is insufficient evidence to support the claim that more than 1% of the DVDs are defective.
D. Reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than 1% of the DVDs are defective.
Question 8 of 40
If a fan purchased a bag with 30 peanuts, what is the lowest level at which this would be a significant event?
A. 0.05
B. 0.025
C. 0.01
D. It is not significant at any of the levels given
Question 11 of 40
A consumer advocacy group claims that the mean amount of juice in a 16
ounce bottled drink is not 16 ounces, as stated by the bottler.
Determine the null and alternative hypotheses for the test described.
A.
H0: µ = 16 ounces Ha: µ < 16 ounces
B.
H0: µ  16 ounces Ha: µ = 16 ounces
C.
H0: µ = 16 ounces Ha: µ 16 ounces
D.
H0: µ = 16 ounces Ha: µ  16 ounces
Question 12 of 40
A poll of 1,068 adult Americans reveals that 52% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 significance level, test the claim that more than half of all voters prefer the Democrat.
A. Reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats.
B. Do not reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats.
C. Reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats.
D. Do not reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats.
Question 13 of 40
A consumer group claims that the mean running time for a certain type of flashlight battery is not the same as the manufacturer’s claims. Determine the null and alternative hypotheses for the test described.
A.
H0: µ = Manufacturer’s claims Ha: µ < Manufacturer’s claims
B.
H0: µ = Manufacturer’s claims Ha: µ  Manufacturer’s claims
C.
H0: µ = Manufacturer’s claims Ha: µ Manufacturer’s claims
D.
H0: µ  Manufacturer’s claims Ha: µ = Manufacturer’s claims
Question 14 of 40
A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 35 such cases from court files and finds that months. Assume that the population standard deviation is 7 months. Test the null hypothesis that µ = 18.7 at the 0.05 significance level.
A.
Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.
B.
Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.
C.
Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.
D.
Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.
Question 15 of 40
The owner of a football team claims that the average attendance at home games is over 4000, and he is therefore justified in moving the team to a city with a larger stadium. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.
A. All games played by the team in question in which the attendance is over 4000
B. All future home games to be played by the team in question
C. All home games played by the team in question
D. None of the populations given are appropriate
Question 16 of 40
A long-distance telephone company claims that the mean duration of long-distance telephone calls originating in one town was greater than 9.4 minutes, which is the average for the state. Determine the conclusion of the hypothesis test assuming that the results of the sampling do not lead to rejection of the null hypothesis.
A. Conclusion: Support the claim that the mean is less than 9.4 minutes.
B. Conclusion: Support the claim that the mean is greater than 9.4 minutes.
C. Conclusion: Support the claim that the mean is equal to 9.4 minutes.
D. Conclusion: Do not support the claim that the mean is greater than 9.4 minutes.
Question 18 of 40
A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?
A. Greater than or equal to 0.10
B. Less than or equal to 0.05
C. Less than or equal to 0.10
D. Greater than or equal to 0.05
Question 19 of 40
A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the conclusion of the hypothesis test assuming that the results of the sampling lead to rejection of the null hypothesis.
A. Conclusion: Support the claim that the mean is equal to 16 ounces.
B. Conclusion: Support the claim that the mean is greater than 16 ounces.
C. Conclusion: Support the claim that the mean is not equal to 16 ounces.
D. Conclusion: Support the claim that the mean is less than 16 ounces.
Question 20 of 40
A psychologist claims that more than 19 percent of the population suffers from professional problems due to extreme shyness. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.
A. The population is all shy workers.
B. The population cannot be identified from the description of the study.
C. The population is all American workers.
D. The population is all American professional workers (doctors, lawyers, CPA’s, and the like..
Question 21 of 40
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
Colorblind Not Colorblind Total
Male 7 53 60
Female 1 39 40
Total 8 92 100
If gender and colorblindness are independent, find the expected values corresponding to the male combinations of gender and colorblindness.
A. Colorblind Male 4.8; Not Colorblind Male 55.2
B. Colorblind Male 6.8; Not Colorblind Male 53.2
C. Colorblind Male 4.8; Not Colorblind Male 55.4
D. Colorblind Male 4.8; Not Colorblind Male 56.2
Question 22 of 40
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
Colorblind Not Colorblind Total
Male 8 52 60
Female 2 38 40
Total 10 90 100
State the null and alternative hypothesis for the test associated with this data.
A.
H0: Colorblindness and gender are dependent characteristics.
Ha: Colorblindness and gender are not related in any way.
B.
H0: Colorblindness and gender are dependent characteristics.
Ha: Colorblindness and gender are related in some way.
C.
H0: Colorblindness and gender are independent characteristics.
Ha: Colorblindness and gender are not related in any way.
D.
H0: Colorblindness and gender are independent characteristics.
Ha: Colorblindness and gender are related in some way.
Question 23 of 40
A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 12 times at the required speed. State the null and alternative hypotheses for this test.
A.
H0: µ 170; Ha: µ = 170
B.
H0: µ < 170; Ha: µ = 170
C.
H0: µ = 170; Ha: µ 170
D.
Question 24 of 40
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
Colorblind Not Colorblind Total
Male 7 53 60
Female 1 39 40
Total 8 92 100
If gender and colorblindness are independent, find the expected values corresponding to the female combinations of gender and colorblindness.
A. Colorblind Female 4.8; Not Colorblind Female 55.2
B. Colorblind Female 3.2; Not Colorblind Female 36.8
C. Colorblind Female 4.8; Not Colorblind Female 35.2
D. Colorblind Female 3.8; Not Colorblind Female 36.2
Question 25 of 40
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
Colorblind Not Colorblind Total
Male 7 53 60
Female 1 39 40
Total 8 92 100
State the null and alternative hypothesis for the information above.
A.
H0: Colorblindness and gender are dependent characteristics.
Ha: Colorblindness and gender are related in some way.
B.
H0: Colorblindness and gender are independent characteristics.
Ha: Colorblindness and gender are not related in any way.
C.
H0: Colorblindness and gender are dependent characteristics.
Ha: Colorblindness and gender are not related in any way.
D.
H0: Colorblindness and gender are independent characteristics.
Ha: Colorblindness and gender are related in some way.
Question 26 of 40
A 95% confidence interval for the mean of a normal population is found to be 13.2 < µ < 22.4. What is the margin of error?
A. 4.6
B. 4.4
C. 4.2
D. 5.6
Question 27 of 40
The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 18 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3? Explain your answer.
A. Smaller. E decreases as the square root of the sample size gets larger.
B. Smaller. E increases as the square root of the sample size gets larger.
C. Larger. E decreases as the square root of the sample size gets larger.
D. Larger. E increases as the square root of the sample size gets larger.
Question 28 of 40
A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 25.2. What is the margin of error?
A. 3.9
B. 4.8
C. 4.9
D. 3.7
Question 29 of 40
Which of the following statements is true?
A. The p distribution cannot be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.
B. The t distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.
C. The t distribution cannot be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.
D. The p distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.
Question 30 of 40
Which of the following statements is true?
A.
The t distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.
B. The p distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.
C. The t distribution cannot be used when finding a confidence interval for the population mean whenever the sample size is small.
D. The p distribution cannot be used when finding a confidence interval for the sample mean whenever the sample size is small.
Question 31 of 40
The following data were analyzed using one-way analysis of variance.
A B C
34 27 19
26 23 31
31 29 22
28 21 22
Which one of the following statements is correct?
A.
The purpose of the analysis is to determine whether the groups A, B, and C are independent.
B. The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.
C. The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal.
D. The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal.
Question 32 of 40
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
Colorblind Not Colorblind Total
Male 8 52 60
Female 2 38 40
Total 10 90 100
If gender and colorblindness are independent, find the expected values corresponding to the four combinations of gender and colorblindness, and enter them in the following table along with row and column totals.
Colorblind Not Colorblind Total
Male
Female
Total
A. Male Colorblind 6.0; Male Not Colorblind 54.0
B. Male Colorblind 7.0; Male Not Colorblind 53.0
C. Male Colorblind 8.0; Male Not Colorblind 52.0
D. Male Colorblind 6.0; Male Not Colorblind 53.0
Question 33 of 40
A large test statistic F tells us that the sample means __________ the data within the individual samples, which would be unlikely if the populations means really were equal (as the null hypothesis claims).
A. differ more than
B. differ less than
C. are equal to
D. do not vary with
Question 34 of 40
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.
The critical value of X2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X2 statistic is 4.613, state your conclusion about the relationship between gender and colorblindness.
A.
Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
B.
Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
C.
Do not Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
D.
Do not Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
Question 35 of 40
A simple random sample from a normal distribution is taken in order to obtain a 95% confidence interval for the population mean. If the sample size is 8, the sample mean x̄ is 22, and the sample standard deviation s is 6.3, what is the margin of error? Show your answer to 2 decimal places.
A. df = 7; E = 3.3445.38 = 5.6566
B. df = 8; E = 3.3445.38 = 5.6566
C. df = 6; E = 2.3656.38 = 5.769
D. df = 7; E = 2.3656.38 = 5.869
Question 36 of 40
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.
The critical value of X2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X2 statistic is 3.427, state your conclusion about the relationship between gender and colorblindness.
A.
Do not reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
B.
Do not reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
C.
Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
D.
Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 12 times at the required speed.
Data from this test had a sample mean of 171.6 yards with a sample standard deviation of 2.4 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer’s requirements. Use the partial t-table below.
Area in one tail
0.025 0.05
Area in two tails
Degrees of
Freedom
n - 1 0.05 0.10
6 2.447 1.943
7 2.365 1.895
8 2.306 1.860
9 2.262 1.833
A.
Accept the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 170 yards.
B. Accept the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 170 yards.
C. Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 170 yards.
D. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 170 yards.
Question 38 of 40
A 95% confidence interval for the mean of a normal population is found to be 17.6 < µ < 23.6. What is the margin of error?
A. 2.0
B. 2.7
C. 3.0
D. 4.0
Question 39 of 40
The following data were analyzed using one-way analysis of variance.
A B C
34 27 19
26 23 21
31 29 22
28 21 12
Which one of the following statements is correct?
A. The purpose of the analysis is to determine whether the groups A, B, and C are independent.
B. The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.
C. The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal.
D. The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal.
Question 40 of 40
The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 25 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3?
A. Smaller. E increases as the square root of the sample size gets larger.
B. Smaller. E decreases as the square root of the sample size gets larger.
C. Larger. E decreases as the square root of the sample size gets larger.
D. Larger. E increases as the square root of the sample size gets larger.