Exam 7: Hypothesis Testing With One Sample

The dean of a major university claims that the mean time for students to earn a Masterʹs degree is at most 4.1 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null Hypothesis?

A trucking firm suspects that the variance for a certain tire is greater than 1,000,000. To check the claim, the firm puts 101 of these tires on its trucks and gets a standard deviation of 1200 miles. If α $\alpha$ = 0.05, test the trucking firmʹs claim using P-values.

Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed. $\text { Claim } \mu \geq 13.9 ; \alpha = 0.05 \text {. Sample statistics: } \bar { x } = 13 , \mathrm {~s} = 1.3 , \mathrm { n } = 10$

Suppose you want to test the claim that $\mu < 65.4 .$ Given a sample size of n = 35 and a level of significance of $\alpha$ α = 0.05, when should you reject H₀?

A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1000 hours. A homeowner selects 25 bulbs and finds the mean lifetime to be 980 hours with a standard deviation of 80 hours. If α $\alpha$ = 0.05, test the manufacturerʹs claim using confidence intervals.

Find the critical value and rejection region for the type of chi-square test with sample size n and level of significance α $\alpha$ Right-tailed test, $\mathrm { n } = 18 , \alpha = 0.01$

Fifty-five percent of registered voters in a congressional district are registered Democrats. The Republican candidate takes a poll to assess his chances in a two-candidate race. He polls 1200 potential voters and finds that 621 plan to vote for the Republican candidate. Does the Republican candidate have a chance to win? Use $\alpha = 0.05$

Test the claim thathat $\sigma ^ { 2 } > 9.5 \text { if } \mathrm { n } = 18 , \mathrm {~s} ^ { 2 } = 13.5 \text {, and } \alpha = 0.01$ .01. Assume that the population is normally distributed.

Suppose you want to test the claim that $\mu$ = 3.5. Given a sample size of n = 40 and a level of significance of $\alpha$ α = 0.05, when should you reject H₀ ?

Find the critical value and rejection region for the type of t-test with level of significance α $\alpha$ and sample size n. Left-tailed test, α $\alpha$ = 0.1, n = 22

Test the claim about the population mean μ at the level of significance α $\alpha$ Assume the population is normally distributed. Claim: $\mu \neq 35 ; \alpha = 0.05 ; \sigma = 2.7$ Sample statistics: $\overline { \mathrm { x } } = 34.1 , \mathrm { n } = 35$

Find the critical value and rejection region for the type of z-test with level of significance α $\alpha$ Left-tailed test, α $\alpha = 0.025$

Find the critical value and rejection region for the type of z-test with level of significance α $\alpha$ Two-tailed test, α $\alpha = 0.10$

Test the claim about the population mean $\mu$ at the level of significance α $\alpha$ . Assume the population is normally distributed. $\text { Claim } \mu = 24 ; \alpha = 0.01 \text {. Sample statistics: } \overline { \mathrm { x } } = 25.2 , \mathrm {~s} = 2.2 , \mathrm { n } = 12$

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 = 1.95 $\alpha$ = 0.05

A telephone company claims that 20% of its customers have at least two telephone lines. The company selects a random sample of 500 customers and finds that 88 have two or more telephone lines. If α = 0.05, test the companyʹs claim using critical values and rejection regions.

Compute the standardized test statistic, $x ^ { 2 }$ 2 to test the claim $\sigma ^ { 2 } \neq 40.8 \text { if } \mathrm { n } = 10 , \mathrm {~s} ^ { 2 } = 45 , \text { and } \alpha = 0.01$

A local brewery distributes beer in bottles labeled 12 ounces. A government agency thinks that the brewery is cheating its customers. The agency selects 20 of these bottles, measures their contents, and obtains a sample mean of 11.7 ounces with a standard deviation of 0.7 ounce. Use a 0.01 significance level to test the agencyʹs claim that the brewery is cheating its customers.

An elementary school claims that the standard deviation in reading scores of its fourth grade students is less than 3.75. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed.

Given $\mathrm { H } _ { 0 } : \mu \leq 25 \text { and } \mathrm { H } _ { \mathrm { a } } : \mu > 25 \text {, }$ determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.