# Statistics

Statistics Project 4

1. The Carolina Tobacco Company advertised that its bestselling nonfiltered cigarettes contain at most 40 mg of nicotine, but Consumer Advocate magazine ran tests of 10 randomly selected cigarettes and found the amounts (in mg) shown in the list below. It’s a serious matter to charge that the company advertising is wrong, so the magazine editor chooses a significance level of α = 0.01 in testing her belief that the mean nicotine content is greater than 40 mg. Using a 0.01 significance level, test the editor’s belief that the mean is greater than 40 mg.

43.3 39.2 41.3 38.1 46.3 43.7 35.2 49.4 40.3 46.6

Show all 5 steps of your hypothesis test including a) the claim being tested, b) the null and alternative hypothesis, c) the test statistic, d) the critical value e) the p value, f) initial conclusion, and g) a final conclusion about the original claim. Be sure to number the 5 steps.

2. Data Set 19 in Appendix B of the textbook (pg 614) contains data from samples of cola cans.

The first column contains weights of regular Coke.

The third column contains weights of Diet Coke.

The fifth column contains weights of regular Pepsi.

You will be conducting two hypothesis tests comparing these data sets. If you follow the 5 steps (be sure to number them) the items below should all be there. For both tests you need to list all of the following items:

a. The claim being tested

b. The Null and Alternative hypotheses

c. Whether this is a lefttailed, righttailed or two tailed test

d. The test statistic

e. The critical value

f. The p value

g. The initial conclusion

h. The final conclusion worded in terms of the original claim

Assume the samples are independent simple random samples selected from normally distributed populations. Do not assume the population standard deviations are equal.

Test 2: Use a .05 significance level to test the claim that the mean weight of regular Coke is equal to the mean weight of regular Pepsi.

If there was a difference in the weights of regular Coke and diet Coke, what is the most likely explanation for this difference?

If there was a difference in the weights of regular Coke and regular Pepsi, what do you think might be an explanation for this difference?

3. The math SAT scores for all women are normally distributed with a mean of 487 and a standard deviation of 95. This question is intended to help you go back and review ideas throughout the book.

a. If a woman who takes the math portion of the SAT is randomly selected, find the probability that her score is above 508.

b. If five math SAT scores are randomly selected from the population of women who take the test, find the probability that all five of the scores are above 508. (Remember the Multiplication Rule from Chapter 4).

c. If five women who take the math portion of the SAT are randomly selected, find the probability that their mean score is above 508.

d. Find P90, the score separating the bottom 90% from the top 10%.

1. The Carolina Tobacco Company advertised that its bestselling nonfiltered cigarettes contain at most 40 mg of nicotine, but Consumer Advocate magazine ran tests of 10 randomly selected cigarettes and found the amounts (in mg) shown in the list below. It’s a serious matter to charge that the company advertising is wrong, so the magazine editor chooses a significance level of α = 0.01 in testing her belief that the mean nicotine content is greater than 40 mg. Using a 0.01 significance level, test the editor’s belief that the mean is greater than 40 mg.

43.3 39.2 41.3 38.1 46.3 43.7 35.2 49.4 40.3 46.6

Show all 5 steps of your hypothesis test including a) the claim being tested, b) the null and alternative hypothesis, c) the test statistic, d) the critical value e) the p value, f) initial conclusion, and g) a final conclusion about the original claim. Be sure to number the 5 steps.

2. Data Set 19 in Appendix B of the textbook (pg 614) contains data from samples of cola cans.

The first column contains weights of regular Coke.

The third column contains weights of Diet Coke.

The fifth column contains weights of regular Pepsi.

You will be conducting two hypothesis tests comparing these data sets. If you follow the 5 steps (be sure to number them) the items below should all be there. For both tests you need to list all of the following items:

a. The claim being tested

b. The Null and Alternative hypotheses

c. Whether this is a lefttailed, righttailed or two tailed test

d. The test statistic

e. The critical value

f. The p value

g. The initial conclusion

h. The final conclusion worded in terms of the original claim

Assume the samples are independent simple random samples selected from normally distributed populations. Do not assume the population standard deviations are equal.

Test 2: Use a .05 significance level to test the claim that the mean weight of regular Coke is equal to the mean weight of regular Pepsi.

If there was a difference in the weights of regular Coke and diet Coke, what is the most likely explanation for this difference?

If there was a difference in the weights of regular Coke and regular Pepsi, what do you think might be an explanation for this difference?

3. The math SAT scores for all women are normally distributed with a mean of 487 and a standard deviation of 95. This question is intended to help you go back and review ideas throughout the book.

a. If a woman who takes the math portion of the SAT is randomly selected, find the probability that her score is above 508.

b. If five math SAT scores are randomly selected from the population of women who take the test, find the probability that all five of the scores are above 508. (Remember the Multiplication Rule from Chapter 4).

c. If five women who take the math portion of the SAT are randomly selected, find the probability that their mean score is above 508.

d. Find P90, the score separating the bottom 90% from the top 10%.

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