Exam 11: Hypothesis Testing for Single Populations

The manager of an insurance company wants to prove that the true average claim is actually higher than $1,800 originally set by the company. He randomly selected 40 claims and determined a sample mean of $1,950. Test the appropriate hypotheses at ? = 0.05 to determine if the insurance company should be concerned. Assume that the standard deviation of claims is $500.

In performing hypothesis tests about the population mean, the population standard deviation should be used if it is known. If it is $\textbf{ not }$ known, which of the following statistical test should be used?

Suppose the alternative hypothesis in a hypothesis test is "the population mean is greater than 60." If the sample size is 80 and alpha =.01, the critical value of z is ___.

Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using $\alpha$ = 0.10, the appropriate decision is ___.

Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of email messages sent by GFS employees are $\textbf{ not }$ business related. A random sample of 300 email messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were $\textbf{ not }$ business related. The null hypothesis is ____.

The executives of CareFree Insurance Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The null hypothesis is ___.

Suppose you are testing the null hypothesis that a population mean is less than or equal to 80, against the alternative hypothesis that the population mean is greater than 80. The sample size is 49 and alpha =.05. If the sample mean is 84 and the population standard deviation is 14, the observed z value is ___.

A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the alternative hypothesis would be ___.

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is $\textbf{ not }$ equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is selected to be 0.10. The critical t value for this problem is ___.

Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 38 defaulted loans. Using $\alpha$ = 0.10, the appropriate decision is ___.

A researcher is testing a hypothesis of a single mean. The critical z value for $\alpha$ =.05 and a two-tailed test is ±1.96. The observed z value from sample data is 2.85. The decision made by the researcher based on this information is to ___ the null hypothesis.

Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of email messages sent by GFS employees are $\textbf{ not }$ business related. A random sample of 300 email messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were $\textbf{ not }$ business related. The appropriate decision is __.

In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is $\textbf{ not }$ equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The level of significance is selected as 0.05. The decision rule for this problem is to reject the null hypothesis if the observed t value is ___.

The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05.

The rejection and non-rejection regions are divided by a point called the critical value.

A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the test statistic would be ___.

Suppose a researcher is testing a null hypothesis that $\mu$ = 61. A random sample of n = 36 is taken resulting in a sample mean of 63 and s = 9. The test statistic is ___.