Quiz 9: Inferences on Two Samples

A garden supplier claims that its new variety of giant tomato produces fruit with an mean weight of 45 ounces. A test is made of $H _ { 0 } : \mu = 45 \text { versus } H _ { 1 } : \mu \neq 45$ The null hypothesis is rejected. State the appropriate conclusion.

A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 25.6 miles per gallon (mpg). A random sample of 54 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 $\mu > 25.6 \mathrm { mpg }$ A test is made of $H _ { 0 } : \mu = 25.6 \text { versus } H _ { 1 } : \mu > 25.6$ Assume that the air filter changes are effective but the conclusion is reached that the chan might not be effective. Which type of error, of any, has occurred?

A grocery store owner claims that the mean amount spent per checkout is more than $\$ 77$ . A test is made of $H _ { 0 } : \mu = 77$ versus $H _ { 1 } : \mu > 77$ . The null hypothesis is not rejected. State the appropriate conclusion.

A grocery store owner claims that the mean amount spent per checkout is more than $\$ 75$ . A test is made of $H _ { 0 } : \mu = 75$ versus $H _ { 1 } : \mu > 75$ . The null hypothesis is rejected. State the appropriate conclusion.

A garden supplier claims that its new variety of giant tomato produces fruit with an mean weight of 44 ounces. A test is made of $H _ { 0 } : \mu = 44 \text { versus } H _ { 1 } : \mu \neq 44$ The null hypothesis is not rejected. State the appropriate conclusion.

A sample of 75 chewable vitamin tablets have a sample mean of 251 milligrams of vitamin C. Nutritionists want to perform a hypothesis test to determine how strong the evidence is that the mean mass of vitamin C per tablet differs from 256 milligrams. State the appropriate null and alternate hypotheses.

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 5 . It is hoped that the new formula may reduce this infestation rate. State the appropriate null and alternate hypotheses.

A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 24 miles per gallon (mpg). A random sample of 60 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 $\mu > 24 \mathrm { mpg }$ A test is made of $H _ { 0 } : \mu = 24 \text { versus } H _ { 1 } : \mu > 24$ Assume that the air filter changes are not effective. Which type of error is impossible?

Determine whether the outcome is a Type I error, a Type II error, or a correct decision. A test is made of $H _ { 0 } : \mu = 18$ versus $H _ { 1 } : \mu \neq 18$ The true value of $\mu$ is 18 and $H _ { 0 }$ not rejected.

A test is made of $H _ { 0 } : \mu = 60 \text { versus } H _ { 1 } : \mu \neq 60$ $\bar { x } = 66$ The population standard deviation is $\sigma = 22$ Compute the value of the test statistic z and determine if $H _ { 0 }$ is rejected at the $\alpha = 0.01 \text { level. }$

A test of $H _ { 0 } : \mu = 55 \text { versus } H _ { 1 } : \mu < 55$ is performed using a significance level of $\alpha = 0.01$ The value of the test statistic is $z = - 2.53 . \text { Is } H _ { 0 }$ rejected?

A test is made of $H _ { 0 } : \mu = 69 \text { versus } H _ { 1 } : \mu \neq 69$ A sample of size n=72 is drawn, and $\bar { x } = 70$ The population standard deviation is $\sigma = 27$ Compute the value of the test statistic z .

Determine whether the outcome is a Type I error, a Type II error, or a correct decision. A test is made of $H _ { 0 } : \mu = 7$ versus $H _ { 1 } : \mu \neq 7$ The true value of $\mu$ is 5 and $\mathrm { H } _ { 0 }$ is rejected.

A test is made of $H _ { 0 } : \mu = 63 \text { versus } H _ { 1 } : \mu > 63$ A sample of size n=68 is drawn, and $\bar { x } = 62$ The population standard deviation is $\sigma = 20$ Compute the value of the test statistic z .

A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 27 miles per gallon (mpg). A random sample of 54 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 $\mu > 27 \mathrm { mpg }$ A test is made of $H _ { 0 } : \mu = 27$ versus $H _ { 1 } : \mu > 27$ Consider these possible conclusions: i). The air filter changes are effective. ii). The air filter changes are not effective. iii). The air filter changes might not be effective. Which of the three conclusions is best if $H _ { 0 }$ is not rejected?

A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 27 miles per gallon (mpg). A random sample of 43 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 $\mu > 27 \text { mpg. }$ A test is made of $H _ { 0 } : \mu = 27 \text { versus } H _ { 1 } : \mu > 27$ Assume that the air filter changes are effective. Which type of error is impossible?

A test is made of $H _ { 0 } : \mu = 44 \text { versus } H _ { 1 } : \mu > 44$ A sample of size n=66 is drawn, and $\bar { x } = 48$ The population standard deviation is $\sigma = 25$ Compute the value of the test statistic z and determine if $H _ { 0 }$ is rejected at the $\alpha = 0.01$ level.

Determine whether the alternative hypothesis is left-tailed, right-tailed, or two-tailed. $H _ { 0 } : \mu = 11 \quad H _ { 1 } : \mu > 11$

A sample of 50 chewable vitamin tablets have a sample mean of 258 milligrams of vitamin C. Nutritionists want to perform a hypothesis test to determine how strong the evidence is that the mean mass of vitamin C per tablet exceeds 260 milligrams. State the appropriate null and alternate hypotheses.

A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 24.7 miles per gallon (mpg). A random sample of 54 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 $\mu > 24.7 \mathrm { mpg }$ . A test is made of $H _ { 0 } : \mu = 24.7$ versus $H _ { 1 } : \mu > 24.7$ Consider these possible conclusions: i). The air filter changes are effective. ii). The air filter changes are not effective. iii). The air filter changes might not be successful. Which of the three conclusions is best if $H _ { 0 }$ is rejected?