Exam 8: Hypothesis Testing

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. Heights of men aged 25 to 34 have a standard deviation of 2.9 . Use a 0.05 significance level to test the claim that the heights of women aged 25 to 34 have a different standard deviation. The heights (in inches) of 16 randomly selected women aged 25 to 34 are listed below. Round the sample standard deviation to five decimal places. 62.13 65.09 64.18 66.72 63.09 61.15 67.50 64.65 63.80 64.21 60.17 68.28 66.49 62.10 65.73 64.72

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s)or P-value (or range of P-values)as appropriate, and state the final conclusion that addresses the original claim. A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.6 minutes with a standard deviation of 2.3 minutes. At the 0.01 significance level, test the claim that the mean waiting time is less than 10 minutes. Use the P-value method of testing hypotheses.

Provide an appropriate response. Complete the following table on hypothesis testing. Test about Distribution Assumptions Mean Median Proportion Variance

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The owner of a football team claims that the average attendance at games is over 523, 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.

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 $n = 17 , \bar { x } = \$ 22,298$ , and $s = \$ 14,200$ . Use a significance level of $\alpha = 0.05$ .

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol $( \mu , p , \sigma )$ for the indicated parameter. The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, $\mu$ , of $48 ^ { \circ } \mathrm { F }$ 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.

A simple random sample of the running time of movies of 70 international movies resulted in a sample mean length of 112 minutes and a sample standard deviation of 7 minutes. Test the claim that international movies have a mean running time of more than 110 minutes at the 5% level of significance. Assume that the lengths of movies are normally distributed.

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol $( \mu , p , \sigma )$ for the indicated parameter. An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.

Find the critical value or values of $\chi ^ { 2 }$ based on the given information. $H _ { 1 } : \sigma < 0.629$ n=19 $\alpha = 0.025$

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P -values) as appropriate, and state the final conclusion that addresses the original claim. A light-bulb manufacturer advertises that the average life for its light bulbs is 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, test the claim that the sample is from a population with a mean life of 900 hours. Use the P-value method of testing hypotheses.

A watch manufacturer believes that 60% of men over age 50 wear watches. So, the manufacturer took a simple random sample of 275 men over age 50 and 170 of those men wore watches. Test the watch manufacturer's claim at $\alpha = .05$

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol $( \mu , p , \sigma )$ for the indicated parameter. An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p , the true proportion of fireflies unable to produce light.

Test the given claim. Use the P -value method or the traditional method as indicated. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s) or P -value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. The mean resting pulse rate for men is 72 beats per minute. A simple random sample of men who regularly work out at Mitch's Gym is obtained and their resting pulse rates (in beats per minute) are listed below. Use a 0.05 significance level to test the claim that these sample pulse rates come from a population with a mean less than 72 beats per minute. Assume that the standard deviation of the resting pulse rates of all men who work out at Mitch's Gym is known to be 6.6 beats per minute. Use the traditional method of testing hypotheses. 54 59 69 84 74 64 69 70 66 80 59 71 76 63

Find the critical value or values of $\chi ^ { 2 }$ based on the given information. $H _ { 1 } : \sigma < 0.629$ n=19 $\alpha = 0.025$

The ____ is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that the null hypothesis is true.

Solve the problem. A hypothesis test is performed to test the claim that a population proportion is greater than 0.7 . Find the probability of a type II error, $\beta$ , given that the true value of the population proportion is 0.72 . The sample size is 50 and the significance level is 0.05 .

Solve the problem. For large numbers of degrees of freedom, the critical $\chi ^ { 2 }$ values can be approximated as follows: $\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 }$ where k is the number of degrees of freedom and z is the critical value. To find the lower critical value, the negative z-value is used, to find the upper critical value, the positive z-value is used. Use this approximation to estimate the critical value of $\chi ^ { 2 }$ in a two-tailed hypothesis test with n=104 and $\alpha = 0.10$

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. Carter Motor Company claims that its new sedan, the Libra, will average better than 32 miles per gallon in the city. 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.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. A consumer advocacy group claims that the mean mileage for the Carter Motor Company's new sedan is less than 32 miles per gallon. Identify the type I error for the test.

Suppose we want to test the claim that less than $1 / 2$ of Americans are in favor of raising the voting age to 21 . Is the hypothesis test left-tailed, right-tailed, or two-tailed?