Question

Using a random sample of n = 50, the sample mean is = 13.5. Suppose that the population standard deviation is

σ=2.5.

Is the above statistical evidence sufficient to make the following claim  μ ≠15:

?o: μ=15

??: μ ≠15

α = 0.05.

p value = 0

Interpret the results using the p value test.

A) Reject Ho.

B) Do not reject Ho.

Answer 1

Solution:- (A) Reject H₀.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 15
Alternative hypothesis: u 15

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 0.3536

z = (x - u) / SE

z = - 4.24

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z statistic less than - 4.24 or greater than 4.24.

Thus, the P-value = less than 0.0001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

(A) Reject H₀.