# Assume a random sample of size

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