Question

True/False Characterize each of the following statements as being true or false.

a. In a hypothesis test, a very high P-value indicates strong support of the alternative hypothesis.

b. The Student t distribution can be used to test a claim about a population mean whenever the sample data are randomly selected from a normally distributed population.

c. When using a x2 distribution to test a claim about a population standard deviation, there is a very loose requirement that the sample data are from a population having a normal distribution.

d. When conducting a hypothesis test about the claimed proportion of adults who have current passports, the problems with a convenience sample can be overcome by using a larger sample size.

e. When repeating the same hypothesis test with different random samples of the same size, the conclusions will all be the same.

Short answer

a. The statement is false.

b. The statement is true.

c. The statement is false.

d. The statement is false.

e. The statement is false.

Step-by-step solution

State the p-value approach in the hypothesis test

a.

The p-value is a probability of getting the values as extreme as the test statistic.

The decision rule is expressed below.

• If the p-value is lesser than the significance level, the null hypothesis will be rejected.
• If the p-value is greater than the significance level, the null hypothesis will be failed to be rejected.

Thus, the high p-value will be supportive of the null hypothesis.

Therefore, the statement will be false.

State the requirements for the student’s t-distribution test

b.

The requirements for the student’s t-distribution test for testing the claim of the population mean are stated below.

• The population is normally distributed, or the sample is larger than 30.
• The sample is a simple random sample.
• The population standard deviation is unknown.

Therefore, the statement will be true.

State the requirements for the chi-square test for the standard deviation 

c.

The requirements for the chi-square test for the standard deviation are as follows.

• The population is normally distributed, which is stricter than the other tests.
• The sample is a simple random sample.

Therefore, the statement is false.

State the requirements for the test for proportions

d.

Simple random samples are collected such that each sample is independent of another.

On the other hand, in convenience sampling, the samples are collected as per the convenience of investigators. Thus, the samples are not random selections.

Thus, a larger sample will not solve the problem of applying the test.

Therefore, the statement is false.

Analyze the results for the hypothesis test

e.

Different samples of the same sizes are collected for the hypothesis test of the same claim.

Different samples result in varied statistics and hence, varying results of the test statistics and hence, the decision.

Thus, the statement is false.