Question

In a test of the hypothesis

Upper H 0 : mu equals 53H0: μ=53

versus

Upper H Subscript a Baseline : mu greater than 53Ha: μ>53​,

a sample of

n equals 100n=100

observations possessed mean

x overbarxequals=52.452.4

and standard deviation

sequals=3.53.5.

Find and interpret the​ p-value for this test.

Answer 1

(a)

H0: = 53

Ha: > 53

n = Sample size = 100

= Sample mean = 52.4

s = 3.5

SE = s/

= 3.5/ = 0.35

Test statistic is:
Z = (52.4 - 53)/0.35 = - 1.7143

Table of Area Under StandardNormal Curve gives area = 0.4564

One tail - Right Side Test

So,

P-value = 0.5 + 0.4564 = 0.9564

So,Answer is:

0.9564

(b) Interpretation of p-value = 0.9564:

P-value is the probability of obtaining an effect at least as extreme as the one in the data, assuming the truth of the null hypothesis.

P-value = 0.9564 determines the statistical significance in the hypothesistest.Here, sincethe p-value is high, we can conclude that the data are likely with True Null Hypothesis: H0: = 53.