Exam 7: Hypothesis Testing With One Sample

Find the critical value and rejection region for the type of z-test with level of significance α. Two-tailed test, α $\alpha = 0.01$

Compute the standardized test statistic, $X ^ { 2 }$ to test the claim $\sigma ^ { 2 } < 11.2 \text { if } \mathrm { n } = 28 , \mathrm {~s} ^ { 2 } = 7 , \text { and } \alpha = 0.10$

You wish to test the claim that $\mu$ = 1430 at a level of significance of α = 0.01 and are given sample statistics $\mathrm { n } = 35 , \overline { \mathrm { x } } = 1400$ Assume the population standard deviation is 82. Compute the value of the standardized test statistic. Round your answer to two decimal places.

Test the claim that $\sigma \neq 23.49 \text { if } \mathrm { n } = 10 , \mathrm {~s} = 24.66 \text {, and } \alpha = 0.01$ Assume that the population is normally distributed.

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha .$ Two-tailed test Z = -1.63 $\alpha$ α = 0.05

Find the standardized test statistic t for a sample with $\mathrm { n } = 12 , \overline { \mathrm { x } } = 31.2 , \mathrm {~s} = 2.2 \text {, and } \alpha = 0.01 \text { if } \mathrm { H } _ { 0 } : \mu = 30$ Round your answer to three decimal places.

The heights (in inches)of 20 randomly selected adult males are listed below. Test the claim that the variance is less than 6.25. Assume the population is normally distributed. Use $\alpha = 0.05$ and P-values. 70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72

Determine whether the normal sampling distribution can be used. The claim is $p \geq 0.675$ and the sample size is n = 42.

Compute the standardized test statistic, $x ^ { 2 }$ to test the claim $\sigma ^ { 2 } = 25.8 \text { if } \mathrm { n } = 12 , \mathrm {~s} ^ { 2 } = 21.6 \text {, and } \alpha = 0.05 \text {. }$

Compute the standardized test statistic, $X ^ { 2 }$ to test the claim $\sigma ^ { 2 } \geq 12.6 \text { if } \mathrm { n } = 15 , \mathrm {~s} ^ { 2 } = 10.5 , \text { and } \alpha = 0.05$

A fast food outlet claims that the mean waiting time in line is less than 3.5 minutes. A random sample of 60 customers has a mean of 3.6 minutes with a population standard deviation of 0.6 minute. If α $\alpha$ = 0.05, test the fast food outletʹs claim using confidence intervals.

A local group claims that the police issue more than 60 speeding 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 are listed below. At α $\alpha$ = 0.02, test the groupʹs claim using confidence intervals. 70 48 41 68 69 55 70 57 60 83 32 60 72 58

The P-value for a hypothesis test is P = 0.034. Do you reject or fail to reject $\mathrm { H } _ { 0 }$ when the level of significance is $\alpha$ = 0.01?

The Metropolitan Bus Company claims that the mean waiting time for a bus during rush hour is less than 5 minutes. A random sample of 20 waiting times has a mean of 3.7 minutes with a standard deviation of 2.1 minutes. At α $\alpha$ = 0.01, test the bus companyʹs claim. Assume the distribution is normally distributed.

Test the claim that $\sigma ^ { 2 } \neq 47.6 \text { if } \mathrm { n } = 10 , \mathrm {~s} ^ { 2 } = 52.5 \text {, and } \alpha = 0.01$ .01. Assume that the population is normally distributed.

Test the claim that $\sigma ^ { 2 } \leq 6.4 \text { if } \mathrm { n } = 20 , \mathrm {~s} ^ { 2 } = 12.4 \text {, and } \alpha = 0.01$ Assume that the population is normally distributed.

Test the claim that $\mu \neq 13 ,$ 13, given that $\sigma = 2.7 , \alpha = 0.05$ and the sample statistics are n = $35 \text { and } \bar { x } = 12.1$ .

Test the claim about the population mean $\mu$ at the level of significance α $\alpha$ Assume the population is normally distributed. $\text { Claim } \mu \leq 6.4 ; \alpha = 0.05 \text {. Sample statistics: } \bar { x } = 6.7 , \mathrm {~s} = 0.8 , \mathrm { n } = 15$

A trucking firm suspects that the mean lifetime of a certain tire it uses is less than 36,000 miles. To check the claim, the firm randomly selects and tests 54 of these tires and gets a mean lifetime of 35,630 miles with a population standard deviation of 1200 miles. At α $\alpha =$ .05, test the trucking firmʹs claim.

Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject $\mathrm { H } _ { 0 }$ for the level of significance α $\alpha$ Right-tailed test Z = 1.43 $\alpha$ = 0.05