Question

Find the value of the standard​ score, z, and determine whether to reject the null hypothesis at a 0.05 significance level. Is the alternative hypothesis​ supported?

H0​: μ=17.5 ​meters, Ha​: μ≠17.5 ​meters, n=49​, x overbar =16.9 ​meters, σ =1.5 meters

The value of the standard score is ____.

(Round to two decimal places)

Find the standard Z score ______.

(Round to two decimal places)

Is the hypothesis test one tailed for two-tailed?

The hypothesis test is ____________

While technology or a standard normal distribution table can be used to find the critical value, in this problem technology will be used.

The critical value is _____.

(Round to two decimal places)

Determine whether the alternative hypothesis is supported at a 0.10 significance level.

A. The standard score is less extreme than the critical​ value(s). Do not reject Upper H 0. The alternative hypothesis is not supported.

B. The standard score is less extreme than the critical​ value(s). Reject Ho. The alternative hypothesis is supported.

C. The standard score is at least as extreme as the critical​ value(s). Do not reject Upper Ho. The alternative hypothesis is not supported.

D. The standard score is at least as extreme as the critical​ value(s). Reject Ho. The alternative hypothesis is supported.

Answer 1

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (16.9 - 17.5)/(1.5/sqrt(49))
z = -2.8

D. The standard score is at least as extreme as the critical​value(s). Reject Ho. The alternative hypothesis is supported.