# Assume a random sample of size

Answer True or False

Assume a random sample of size n is available from a normal population. Assume the null hypothesis is that the population mean is zero versus the alternative hypothesis that it is not zero. Assume a single sample t test is used for hypothesis testing. If the sample size does not change, and the Type I error rate is changed from 5% to 1%, then the Type II error rate will increase. Answer True or False.

True

False

Question 2

Assume the population has a normal distribution and the number of observations in a random sample is greater than fifty. If a z test is going to be used to test a null hypothesis, what is the critical value for a two-tailed test if the type one-error rate is 0.01?

+-2.052

+-1.645

+-2.576

+-2.33

Question 3

use the degree of confidence and sample data to construct a confidence interval for the population proportion p.

n = 56, x = 30; 95% confidence (Use the procedure in Business Statistics Section 8.3.)

0.405 < p < 0.666

0.403 < p < 0.669

0.425 < p < 0.647

0.426 < p < 0.646

Question 4

use the given data to find the sample size required to estimate the population proportion.

Margin of error: 0.005; confidence level: 96%; p and q unknown. Use z = 2.05.

42,025

32,024

42,148

42,018

Question 5

Multiple Choice

Which of the following statements is not true?

If the sample size is held constant and the same test statistic is used, the type I error rate can be changed and not affect the power of the test.

The sampling distribution of a statistic is the probability distribution for that statistic based on all possible random samples from a population.

A symmetric, heavy-tailed distribution may be detected using a boxplot and QQ chart.

Bootstrapping depends on sampling with replacement.

Question 6

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.

n = 10, x̄ = 8.1, s = 4.8, 95% confidence

5.32 < µ < 10.88

4.67 < µ < 11.53

4.61 < µ < 11.59

4.72 < µ < 11.48

Question 7

use the information to find the sample size required to estimate an unknown population mean µ.

Margin of error: $135, confidence level: 95%, σ = $500

74

37

53

46

Question 8

Solve the problem.

A 99% confidence interval (in inches) for the mean height of a population is 65.7 < µ < 67.3. This result is based on a sample of size 144. Construct the 95% confidence interval. (Hint: you will first need to find the sample mean and sample standard deviation).

66.2 in < µ < 66.8 in.

65.9 in < µ < 67.1 in.

65.7 in < µ < 67.3 in.

65.6 in < µ < 67.4 in.

Question 9

Multiple Choice

Which of the following statements is not true for sampling distributions?

An accurate sampling distribution for the mean statistic can always be identified based on a single sample without regard for sample size or knowledge of the population sampled.

A sampling distribution is necessary for making confidence statements about an unknown population parameter.

Depending on the population, it may not be possible to express the sampling distribution for a statistic in closed form mathematically.

A sampling distribution depends on the nature of the population being sampled.

Question 10

Assume normality and use the information given to find the p-value. Based on the p-value estimated, determine if the null hypothesis should be rejected at a 0.1 significance level. Select the correct answer if the test statistic in a two-tailed test is z= -1.63. Follow the procedure shown in Business Statistics.

p-value = 0.9484; fail to reject the null hypothesis

p-value = 0.0516; reject the null hypothesis

p-value = 0.0516; fail to reject the null hypothesis

p-value = 0.0258; reject the null hypothesis

Assume a random sample of size n is available from a normal population. Assume the null hypothesis is that the population mean is zero versus the alternative hypothesis that it is not zero. Assume a single sample t test is used for hypothesis testing. If the sample size does not change, and the Type I error rate is changed from 5% to 1%, then the Type II error rate will increase. Answer True or False.

True

False

Question 2

Assume the population has a normal distribution and the number of observations in a random sample is greater than fifty. If a z test is going to be used to test a null hypothesis, what is the critical value for a two-tailed test if the type one-error rate is 0.01?

+-2.052

+-1.645

+-2.576

+-2.33

Question 3

use the degree of confidence and sample data to construct a confidence interval for the population proportion p.

n = 56, x = 30; 95% confidence (Use the procedure in Business Statistics Section 8.3.)

0.405 < p < 0.666

0.403 < p < 0.669

0.425 < p < 0.647

0.426 < p < 0.646

Question 4

use the given data to find the sample size required to estimate the population proportion.

Margin of error: 0.005; confidence level: 96%; p and q unknown. Use z = 2.05.

42,025

32,024

42,148

42,018

Question 5

Multiple Choice

Which of the following statements is not true?

If the sample size is held constant and the same test statistic is used, the type I error rate can be changed and not affect the power of the test.

The sampling distribution of a statistic is the probability distribution for that statistic based on all possible random samples from a population.

A symmetric, heavy-tailed distribution may be detected using a boxplot and QQ chart.

Bootstrapping depends on sampling with replacement.

Question 6

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.

n = 10, x̄ = 8.1, s = 4.8, 95% confidence

5.32 < µ < 10.88

4.67 < µ < 11.53

4.61 < µ < 11.59

4.72 < µ < 11.48

Question 7

use the information to find the sample size required to estimate an unknown population mean µ.

Margin of error: $135, confidence level: 95%, σ = $500

74

37

53

46

Question 8

Solve the problem.

A 99% confidence interval (in inches) for the mean height of a population is 65.7 < µ < 67.3. This result is based on a sample of size 144. Construct the 95% confidence interval. (Hint: you will first need to find the sample mean and sample standard deviation).

66.2 in < µ < 66.8 in.

65.9 in < µ < 67.1 in.

65.7 in < µ < 67.3 in.

65.6 in < µ < 67.4 in.

Question 9

Multiple Choice

Which of the following statements is not true for sampling distributions?

An accurate sampling distribution for the mean statistic can always be identified based on a single sample without regard for sample size or knowledge of the population sampled.

A sampling distribution is necessary for making confidence statements about an unknown population parameter.

Depending on the population, it may not be possible to express the sampling distribution for a statistic in closed form mathematically.

A sampling distribution depends on the nature of the population being sampled.

Question 10

Assume normality and use the information given to find the p-value. Based on the p-value estimated, determine if the null hypothesis should be rejected at a 0.1 significance level. Select the correct answer if the test statistic in a two-tailed test is z= -1.63. Follow the procedure shown in Business Statistics.

p-value = 0.9484; fail to reject the null hypothesis

p-value = 0.0516; reject the null hypothesis

p-value = 0.0516; fail to reject the null hypothesis

p-value = 0.0258; reject the null hypothesis

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