Exam 8: Hypothesis Testing

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.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. -A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 2 in a thousand. Identify the type I error for the test.

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. -With individual lines at the checkouts, a store manager finds that the standard deviation for the waiting times on Monday mornings is 5.7 minutes. After switching to a single waiting line, he finds that for a random sample of 29 customers, the waiting times have a standard deviation of 4.9 minutes. Use a 0.025 significance level to test the claim that with a single line, waiting times vary less than with individual lines.

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (µ, p, ?) 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°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.

Suppose that you wish to test a claim about a population mean. Which distribution should be used given that the sample is a voluntary response sample, $\sigma$ is unknown, n = 15, and the population is normally distributed?

Find the P-value for the indicated hypothesis test. -An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 18 were no-shows. Find the P-value for a test of the airline's claim.

Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). - $\text { With } \mathrm { H } _ { 1 } : p > 0.249 \text {, the test statistic is } \mathrm { z } = 0.41 \text {. }$

Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). -The test statistic in a two-tailed test is z = 1.95.

Provide an appropriate response -In a population, 11% of people are left handed. In a simple random sample of 160 people selected from this population, the proportion of left handers is 0.10. What is the number of left handers in the sample and what notation is given to that number? What are the values of p and $\hat p$ ?

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. -In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures. 518 548 561 523 536 499 538 557 528 563 At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours. Use the P-value method of testing hypotheses.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. -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 $\mathrm { k }$ is the number of degrees of freedom and $\mathrm { z }$ 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 right-tailed hypothesis test with $\mathrm { n } = 146$ and $\alpha = 0.01$

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%.

Find the value of the test statistic z using $z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } }$ -The claim is that the proportion of accidental deaths of the elderly attributable to residential falls is more than 0.10, and the sample statistics include n = 800 deaths of the elderly with 15% of them attributable to residential falls.

Define Type I and Type II errors. Give an example of a Type I error which would have serious consequences. Give an example of a Type II error which would have serious consequences. What should be done to minimize the consequences of a serious Type I error?

Find the critical value or values of $\chi ^ { 2 }$ based on the given information. - :\sigma>26.1 =9 \alpha=0.01

Find the value of the test statistic z using z $z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } }$ -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 = 575 drowning deaths of children with 30% of them attributable to beaches.

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 left-tailed test.

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (µ, p, ?) for the indicated parameter. -A researcher claims that 62% of voters favor gun control.

A manufacturer finds that in a random sample of 100 of its CD players, 96% have no defects. The manufacturer wishes to make a claim about the percentage of nondefective CD players and is prepared to exaggerate. What is the highest rate of nondefective CD players that the manufacturer Could claim under the following condition? His claim would not be rejected at the 0.05 significance level if this sample data were used. Assume that a left-tailed hypothesis test would be performed.

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%.