Use technology to help you test the claim about the population? mean, muμ?, at the given level of? significance, alphaα?, using the given sample statistics. Assume the population is normally distributed.

Claim:

μ>1270?; α=0.02?; σ=199.23. Sample? statistics: x =1291.16, n= 250

a) Identify the null and alternative hypotheses. Choose the correct answer below. Calculate the standardized test statistic.

b) The standardized test statistic is___ (Round to two decimal places as? needed.)

c) Determine the? P-value. P = ___ (Round to three decimal places as? needed.) Determine the outcome and conclusion of the test.

d) Fail to reject or reject H0. At the 2?% significance? level, there is or is not enough evidence to support or reject the claim.