Exam 8: Hypothesis Testing

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. -A random sample of 100 pumpkins is obtained and the mean circumference is found to be 40.5 cm. Assuming that the population standard deviation is known to be 1.6 cm, use a 0.05 significance level to test the claim that the mean circumference of all pumpkins is equal to 39.9 cm.

Find the P-value for the indicated hypothesis test. -A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 97 such fax machines, 5% are defective. Find the P-value for a test of the manufacturer's claim.

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. -A machine dispenses a liquid drug into bottles in such a way that the standard deviation of the contents is 81 milliliters. A new machine is tested on a sample of 24 containers and the standard deviation for this sample group is found to be 26 milliliters. At the 0.05 level of significance, test the claim that the amounts dispensed by the new machine have a smaller standard deviation.

Provide an appropriate response. -Compare the steps in the traditional method of hypothesis testing with the steps in the P-value method of hypothesis testing. How are they alike and how are they different? Traditional Method P-value Method Comparison

Find the P-value for the indicated hypothesis test. -A random sample of 139 forty-year-old men contains 26% smokers. Find the P-value for a test of the claim that the percentage of forty-year-old men that smoke is 22%.

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 female college students, the mean weight is given by $\mu = 132$ lb. Sample data are summarized as $\mathrm { n } = 20 , \overline { \mathrm { x } } = 137 \mathrm { lb }$ , and $\mathrm { s } = 14.2 \mathrm { lb }$ . Use a significance level of $\alpha = 0.1$ .

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test -The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, $\mu$ , of $50 ^ { \circ } \mathrm { F }$ , ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Identify the type I error for the test.

Use the given information to find the P-value -The test statistic in a two-tailed test is z = -1.63.

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. 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.

Find the P-value for the indicated hypothesis test. -A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the school's students, 32% of them plan to go into general practice. Find the P-value for a test of the school's claim.

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter. -The principal of a middle school claims that test scores of the seventh-graders at her school vary less than the test scores of seventh-graders at a neighboring school, which have variation described by $\sigma = 14.7$ .

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. - $\alpha = 0.05$ for a two-tailed test.

Solve the problem. -What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the rare event rule and make a subjective estimate to determine whether the event is likely. Claim: An employee of a company is equally likely to take a sick day on any day of the week. Last year, the total number of sick days taken by all the employees of the company was 143. Of these, 52 were Mondays, 14 were Tuesdays, 17 were Wednesdays, 17 were Thursdays, and 43 were Fridays.

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 lifetime of car engines of a particular type is greater than 220,000 miles. Sample data are summarized as $n = 23 , \bar { x } = 226,450$ miles, and $s = 11,500$ miles. Use a significance level of $\alpha = 0.01$ .

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. -A nationwide study of American homeowners revealed that $64 \%$ have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Can the value $0.64$ be rejected if a survey of 490 homes in Omaha yields 331 with one or more lawn mowers? Use ?=0.05

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. -In a sample of 167 children selected randomly from one town, it is found that 37 of them suffer from asthma. At the 0.05 significance level, test the claim that the proportion of all children in the town who suffer from asthma is 11%.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test -A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the $\sigma = 3.3$ claimed by the manufacturer. Identify the type II error for the test.

Express the null hypothesis $\mathrm { H } _ { 0 }$ and the alternative hypothesis $\mathrm { H } _ { 1 }$ in symbolic form. Use the correct symbol ( $\mu , \mathrm { p }$ , $\sigma$ )for the indicated parameter. -Carter Motor Company claims that its new sedan, the Libra, will average better than 30 miles per gallon in the city. Use $\mu$ , the true average mileage of the Libra.

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 adult population of one town, the mean annual salary is given by $\mu = \$ 30,000$ . Sample data are summarized as $\mathrm { n } = 17 , \overline { \mathrm { x } } = \$ 22,298$ , and $\mathrm { s } = \$ 14,200$ . Use a significance level of $\alpha = 0.05$ .

Solve the problem. -Use the P-value method to test the claim that the population standard deviation of the systolic blood pressures of adults aged 40-50 is equal to $22 \mathrm { mmHg }$ . The sample statistics are as follows: $\mathrm { n } = 23 , \overline { \mathrm { x } } = 132.3 \mathrm { mmHg }$ , $\mathrm { s } = 26.7 \mathrm { mmHg }$ . Be sure to state the hypotheses, the value of ths test statistic, the P-value, and your conclusion. Use a signifiance level of $0.05$ .