Question

Use technology to help you test the claim about the population mean, μ, at the given level of significance, α, using the given sample statistics. Assume the population is normally distributed. Claim: μ> 1 180: α 0.02; σ 211.79. Sample statistics: x 1203.69, n 250 ldentify the null and alternative hypotheses. Choose the correct answer below ) B. H0: μ s 1180 Ha : μ> 1180 Ha: μ 1203.69 HH 1180 Ha H 1180 O c. HOHs 1203 D. Ho : μ> 1203.69 Ha H 1203.69 НО:p2 1203.69 Ha : μ< 1203.69 О Е, O F. Ho: H 1180 Calculate the standardized test statistic. The standardized test statistic is Round to two decimal places as needed.) Determine the P-value P(Round to three decimal places as needed.) Determine the outcome and conclusion of the test. HO. At the 2% significance level, there | 'I enough evidence to the claim

Answer 1

Sample size = n = 250

Sample mean = = 1203.69

Population standard deviation = = 211.79

The null and alternative hypothesis is

Level of significance = 0.02

Here population standard deviation is known so we have to use z-test statistic.

By using the technology we have to solve this question.

By using Ti-84 calculator we can solve this question easily.

Click on STAT ------> TESTS ------->Z-Test ------->Stats ------->Enter values ------->

$mu_{0}$: 1180

: 211.79

: 1203.69

n: 250

$mu:>mu_{0}$

Calculate

We get z = 1.77

THe standardized test statistic is 1.77

The p-value is

p = 0.038

P-value > 0.02 we fail to reject null hypothesis.

Fail to reject H0. At the 2% significance level, there is enough evidence to reject the claim.