Exam 8: Hypothesis Testing

A psychologist claims that more than 75 percent of the population suffers from professional problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

Use the given information to find the P-value -The test statistic in a two-tailed test is z = 1.95.

Find the P-value for the indicated hypothesis test. -An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 225 fathers from Littleton, yielded 97 who did not help with child care. Find the P-value for a test of the researcher's claim.

Find the P-value for the indicated hypothesis test. -A nationwide study of American homeowners revealed that 65% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Find the P-value for a test of the claim that the proportion with lawn mowers in Omaha is higher than 65%. Among 497 randomly selected homes in Omaha, 340 had one or more lawn mowers.

Use the given information to find the P-value -The test statistic in a left-tailed test is z = -2.05.

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion. -A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30 g. The mean weight for a random sample of 16 ball bearings is 29 g with a standard deviation of 3.9 g. At the 0.05 significance level, test the claim that the mean is less than 30 g.

Find the critical value or values of x $x ^ { 2 }$ based on the given information. - :\sigma9.3 =28 \alpha=0.05

Assume that 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. - $\alpha = 0.09$ for a right-tailed test.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test -The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of seventh-graders at a neighboring school, which have variation described by $\sigma = 14.7$ Identify the type I error for the test.

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion. -A researcher wants to check the claim that convicted burglars spend an average of $18.7$ months in jail. She takes a random sample of 11 such cases from court files and finds that $\bar { x } = 20.5$ months and $s = 7.9$ months. Test the null hypothesis that $\mu = 18.7$ at the $0.05$ significance level.

Provide an appropriate response. -Describe how to write the null and alternative hypotheses based on a claim. You may give an example to clarify your explanation.

Provide an appropriate response. - $\text { Under what conditions do you reject } \mathrm { H } _ { 0 } \text { ? Discuss both the traditional and the } \mathrm { P } \text {-value approach. }$

Find the critical value or values of x $x ^ { 2 }$ based on the given information. - :\sigma=8.0 n=10 \alpha=0.01

Use the given information to find the P-value -The test statistic in a left-tailed test is z = -1.83.

The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by $\sigma = 14.7$ . Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

Use the given information to find the P-value -The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n = 647 drowning deaths of children with 30% of them attributable to beaches.

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion. -Test the claim that the mean age of the prison population in one city is less than 26 years. Sample data are summarized as $\mathrm { n } = 25 , \overline { \mathrm { x } } = 24.4$ years, and $\mathrm { s } = 9.2$ years. Use a significance level of $\alpha = 0.05$

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion. -A light-bulb manufacturer advertises that the average life for its light bulbs 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours. 995 590 510 539 739 917 571 555 916 728 664 693 708 887 849 At the 10% significance level, do the data provide evidence that the mean life for the company's light bulbs differs from the advertised mean?

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion. -Test the claim that for the population of history exams, the mean score is 80 . Sample data are summarized as $\mathrm { n } = 16 , \overline { \mathrm { x } } = 84.5$ , and $\mathrm { s } = 11.2$ . Use a significance level of $\alpha = 0.01$

The owner of a football team claims that the average attendance at games is over 727, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.