Exam 8: Hypothesis Testing

A lab technician is tested for her consistency by making multiple measurements of the cholesterol level in one blood sample. The target precision is a standard deviation of $1.2 \mathrm { mg } / \mathrm { dL }$ or less. If 12 measurements are taken and the standard deviation is $2.1 \mathrm { mg } / \mathrm { dL }$ , is there enough evidence to support the claim that her standard deviation is greater than the target, at $\alpha = 0.01$ ?

A random sample of 450 shoppers at Quincy Mall found that 125 favored longer shopping hours. Is this sufficient evidence at the 0.05 level of significance to conclude that less than 30% of the shoppers at Quincy Mall favor longer hours?

State the appropriate null and alternative hypothesis and find the critical values for a two-tailed test with $\alpha = 0.10$ and $n = 8$ . Use $\sigma ^ { 2 } = 196$ .

The following display from a TI-84 Plus calculator presents the results of a hypothesis tes What is the value of the test statistic?

A random sample of heights (in feet) of active volcanoes in North America, outside of Alaska , is shown. Is there sufficient evidence that the standard deviation in heights of volcanoes outside of Alaska is less than the standard deviation in heights of Alaskan volcanoes, which is $2385.9$ feet? Use $\alpha = 0.05$ .

A new organic pest control formula is being tested on potato plants to see whether it can reduce the level of potato beetle infestation. The mean number of beetles per untreated Plant is 7. It is hoped that the new formula may reduce this infestation rate. State the Appropriate null and alternate hypotheses.

An average computer mouse inspector can inspect 60 mice per hour with a population standard deviation of 8 mice per hour. The 48 computer mice inspectors at a particular factory can only inspect 55 mice per hour. Does the company have reason to believe that these inspectors are slower than average at $\alpha = 0.10$ ?

The Eagle Ridge Contractors Association claims the average price of a home in their subdivision is $125,150 with a standard deviation of $7,350. A sample of 36 homes for Sale in this subdivision had an average selling price of $123,550. The Eagle Ridge Home Owners Association is interested in knowing if the costs of homes for sale in this Subdivision are actually lower than claimed? What is the p-value for this left-tailed test?

For the conjecture "The average rent of an apartment is more than $950 per month," the alternative hypothesis is:

A test of $H _ { 0 } : \mu = 42$ versus $H _ { 1 } : \mu < 42$ is performed using a significance level of $\alpha = 0.05$ . The value of the test statistic is $z = - 1.47$ . Is $H _ { 0 }$ rejected?

The Golden Comet is a hybrid chicken that is prized for its high egg production rate and gentle disposition. According to recent studies, the mean rate of egg production for 1-year-old Golden Comets is $5.6$ eggs/week. Sarah has 47 1-year-old hens that are fed exclusively on natural scratch feed: insects, seeds, and plants that the hens obtain as they range freely around the farm. Her hens exhibit a mean egg-laying rate of $6.1 \mathrm { eggs } /$ day. Sarah wants to determine whether the mean laying rate $\mu$ for her hens is higher than the $m$ rate for all Golden Comets. State the appropriate null and alternate hypotheses.

A test of $H _ { 0 } : \mu = 50$ versus $H _ { 1 } : \mu \neq 50$ is performed using a significance level of $\alpha = 0.05$ . The value of the test statistic is $z = - 1.88$ . Is $H _ { 0 }$ rejected?

A random sample of second-round gold scores from a major tournament is listed below. At $\alpha = 0.10$ , is there sufficient evidence to conclude that the population variance exceeds 74 82 76 74 78 77 81 82 74 75

Researchers suspect that $17 \%$ of all high school students smoke at least one pack of cigarettes a day. At Wilson High School, a randomly selected sample of 300 students found that 49 students smoke at least one pack of cigarettes a day. At $\alpha = 0.05$ , test the claim that less than $17 \%$ of all high school students smoke at least one pack of cigarettes a day. Use the $P$ -value method.

A grocery store owner claims that the mean amount spent per checkout is more than $\$ 56$ A test is made of $H _ { 0 } : \mu = 56$ versus $H _ { 1 } : \mu > 56$ . The null hypothesis is rejected. State the appropriate conclusion.

Stating the hypothesis should be the first step used in hypothesis testing.

A machine that fills beverage cans is supposed to put 16 ounces of beverage in each can. Following are the amounts measured in a simple random sample of eight cans. 16.04 15.96 15.84 16.08 15.79 15.90 15.89 15.70 Assume that the sample is approximately normal. Can you conclude that the mean volum from 16 ounces? Use the $\alpha = 0.01$ level of significance. me differs

A test of $H _ { 0 } : \mu = 53$ versus $H _ { 1 } : \mu \neq 53$ is performed using a significance level of $\alpha = 0.01$ . The $P$ -value is $0.033$ . If the true value of $\mu$ is 53 , does the conclusion result in a Type I error, a Type II error, or correct decision?

A political strategist claims that $56 \%$ of voters in Madison County support his candidate. In a poll of 300 randomly selected voters, 150 of them support the strategist's candidate. At $\alpha = 0.05$ , is the political strategist's claim warranted?