Exam 8: Hypothesis Testing

Mercury is a heavy metal that can cause severe health problems in even small concentratiı Fish and shellfish efficiently concentrate mercury into their flesh, so it is important to mo seafood for its mercury content. An extensive study conducted in 1980 concluded that the mean mercury level in oysters $\mathrm { f }$ White Bear estuary was $0.020$ parts per million (ppm) with a standard deviation $\sigma = 0.022$ ppm. In 2012 , a sample of 48 oysters from the same estuary exhibited a mean mercury concentration of $0.004$ ppm. Can you conclude that the 2012 mercury concentration is lower than in 1980 ? Use the $\alpha = 0.01$ level of significance. ns.

In a particular city, the average annual salary for secretaries is $28,000. A sample of secretaries from Company A shows an average annual salary of $24,500 with a Population standard deviation of $4500. Secretaries at Company A claim they are paid Less than the city average. What is the test value for this claim?

A sample of 35 students enroll in a program that claims to improve scores on the quantita reasoning portion of the Graduate Record Examination (GRE). The participants take a mc GRE test before the program begins and again at the end to measure their improvement. The mean number of points improved was $\bar { x } = 20$ . Assume the standard deviation is $\sigma = 64$ and let $\mu$ be the population mean number of points improved. To determine whether the program is effective, a test is made of the hypotheses $H _ { 0 } : \mu = 0$ versus $H _ { 1 } : \mu > 0$ . Do you reject $H _ { 0 }$ at the $\alpha = 0.01$ level? ive

Use technology to find the $P$ -value for the following values of the test statistic $t$ , sample size $n$ , and alternate hypothesis $H _ { 1 }$ . $t = 1.247 , n = 10 , H _ { 1 } : \mu > \mu _ { 0 }$

A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of $23.4$ miles per gallon (mpg). A random sample of 56 cars are selected and the air filter of each is replaced with a new one. Let $\mu$ be the population mean fuel efficiency score that would occur if every car's air filter were replaced. The air filter change is deemed effective if $\mu > 23.4$ mpg. A test is made of $H _ { 0 } : \mu = 23.4$ versus $H _ { 1 } : \mu > 23.4$ . Assume that the air filter changes are not effective. Which type of error is impossible?

A sample of 35 students enroll in a program that claims to improve scores on the quantita reasoning portion of the Graduate Record Examination (GRE). The participants take a mc GRE test before the program begins and again at the end to measure their improvement. The mean number of points improved was $\bar { x } = 10$ . Assume the standard deviation is $\sigma = 46$ and let $\mu$ be the population mean number of points improved. To determine whether the program is effective, a test is made of the hypotheses $H _ { 0 } : \mu = 0$ versus $H _ { 1 } : \mu > 0$ . Compute the $P$ -value. ive

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population mean $\mu$ . How many degrees of freedom are there?

A test of $H _ { 0 } : \mu = 53$ versus $H _ { 1 } : \mu < 53$ is performed using a significance level of $\alpha = 0.01$ . The $P$ -value is $0.124$ . If the true value of $\mu$ is 49 , does the conclusion result in a Type I error, a Type II error, or correct decision?

An average department store sells 150 men's suits per year. The men's suit departments at a particular national chain of stores claim they sell more than the industry average. In 45 of their stores, they sold, on the average, 250 suits per year with a population standard Deviation of 30. What is the test value for their claim?

State the appropriate null and alternative hypothesis and find the critical value for a left-tailed test with $\alpha = 0.10$ and $n = 23$ . Use $\sigma ^ { 2 } = 225$ .

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population mean $\mu$ . What is the value of $\bar { x }$ ?

For the conjecture "The average weight of a cuckoo bird is less than 1.6 pounds", the null and alternative hypotheses are:

A test of $H _ { 0 } : \mu = 56$ versus $H _ { 1 } : \mu \neq 56$ is performed using a significance level of $\alpha = 0.05$ . The $P$ -value is $0.016$ . If the true value of $\mu$ is 54 , does the conclusion result in a Type I error, a Type II error, or correct decision?

At a certain university, the average attendance at basketball games has been 2725. This year the attendance for the first 14 games has been 2265 with a standard deviation of 485) The athletic director claims that the attendance is the same as last year. If α = 0.05, What are the critical values for this two-tailed t test?

Using the $z$ table, determine the critical values for a two-tailed test when $\alpha = 0.03$ .

If the probability of a type II error in a hypothesis test is $0.40$ , and $\alpha = 0.08$ , then the power of this test is

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population proportion $p$ . What is the value of the sample proportion $\hat { p }$ ?

Sandra Johnson, a researcher, believes her pulse rate will decrease with exercise. Her alternative hypothesis would contain an equal sign.

The following display from a TI-84 Plus calculator presents the results of a hypothesis tes Do you reject $H _ { 0 }$ at the $\alpha = 0.05$ level?