Exam 10: Hypothesis Tests Regarding a Parameter

Test the claim that $\sigma ^ { 2 } < 50.4 \text { if } n = 28 , s ^ { 2 } = 31.5 , \text { and } \alpha = 0.10$ Assume that the population is normally distributed,

Test the claim that Assume that the population is normally distributed.

The mean age of professors at a university is greater than 58.3 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

The mean repair bill of cars is greater than $110. Write the null and alternative hypotheses.

A local group claims that the police issue at least 60 parking tickets a day in their area. To prove their point,they randomly select two weeks. Their research yields the number of tickets issued for each day. The data arelisted below. At α = 0.01, test the groupʹs claim. Round the test statistic to the nearest thousandth. 70 48 41 68 69 55 70 57 60 83 32 60 72 58

The mean age of principals in a local school district is 50.2 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

It has been estimated that the G-car obtains a mean of 40 miles per gallon on the highway, and the company that manufactures the car claims that it exceeds this estimate in highway driving. To support its assertion, the company randomly selects 36 G-cars and records the mileage obtained for each car over a driving course similar to that used to obtain the estimate. The following data resulted: miles per gallon, s=6 miles per gallon. Calculate the value of if the true value of the mean is really 42 miles per gallon. Use

It is desired to test H0: μ = 12 against H1: μ ≠ 12 using α = 0.05. The population in question is uniformlydistributed with a standard deviation of 2.0. A random sample of 100 will be drawn from this population. If μis really equal to 11.9, what is the value of β associated with this test?

Suppose you want to test the claim that $\mu = 3.5 .$ Given a sample size of n=48 and a level of significance of $\alpha$ =0.01 , when should you reject H₀ ?

Determine the critical value for a left-tailed test of a population standard deviation for a sample of size n = 21at the α = 0.05 level of significance.

What is the probability associated with not making a Type II error?

The mean number of rushing yards for one NFL team was less than 99 yards per game. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

Compute the standardized test statistic, $x ^ { 2 }$ to test the claim $\sigma ^ { 2 } = 30.1 \text { if } n = 12 , s ^ { 2 } = 25.2 \text {, and } \alpha = 0.05 \text {. }$

Determine the critical values for a two-tailed test of a population mean at the α = 0.01 level of significancebased on a sample size of n = 29.

Compute the standardized test statistic, $\chi ^ { 2 }$ to test the claim $\sigma ^ { 2 } > 15.2 \text { if } \mathrm { n } = 18 , \mathrm {~s} ^ { 2 } = 21.6 \text {, and } \alpha = 0.01$

The weights (in ounces) of a sample of tomatoes of a particular variety are summarized in the boxplot below.Based on the boxplot, is a large sample necessary to conduct a hypothesis test about the mean weight? If so,why?

$\mathrm { H } _ { 0 } : \sigma = 8.6$ $\mathrm { H } _ { 1 } : \sigma < 8.6$

Find the standardized test statistic t for a sample with $\mathrm { n } = 12 , \overline { \mathrm { x } } = 30.2 , \mathrm {~s} = 2.2 , \text { and } \alpha = 0.01 \text { if } \mathrm { H } _ { 0 } : \mu = 29 . \text { Round }$ your answer to three decimal places.

Find the critical value for a two-tailed test with α = 0.08.

When the results of a hypothesis test are determined to be statistically significant, then we _______________ thenull hypothesis.