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Question 1
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 data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis if the type one-error rate is 0.1 for a two-tailed test.
+-2.052
+-1.4805
+-1.645
+-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
use the given data to find the sample size required to estimate the population proportion.
Margin of error: 0.04; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 60%.
577
519
1441
996
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
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation and pick the closest answer.
Weights of men: 90% confidence; n = 14, x̄ = 161.5 lb, s = 13.7 lb
10.4 lb < sigma < 20.3 lb
10.2 lb < sigma < 19.3 lb
10.8 lb < sigma < 17.7 lb
11.1 lb < sigma < 20.7 lb
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 = 0.0516; reject the null hypothesis
p-value = 0.1031; reject the null hypothesis
p-value = 0.1031; fail to reject the null hypothesis
p-value = 0.0516; fail to reject the null hypothesis
