Question

Use technology to help you test the claim about the population​ mean,

mu
μ​, at the given level of​ significance,
alpha
α​, using the given sample statistics. Assume the population is normally distributed.

​Claim:
mu
μ
greater than
>
1180
1180​;
alpha
α
equals
=
0.02
0.02​;
sigma
σ
equals
=
201.71
201.71. Sample​ statistics:
x overbar
x
equals
=
1198.79
1198.79​, n
equals
=
200
200
Identify the null and alternative hypotheses. Choose the correct answer below.


E.
Upper H 0
H0​:
mu
μ
less than or equals
≤
1180
1180
Upper H Subscript a
Ha​:
mu
μ
greater than
1180
Your answer is correct.
F.
Upper H 0
H0​:
mu
μ
greater than or equals
≥
1198.79
1198.79
Upper H Subscript a
Ha​:
mu
μ
less than
<
1198.79

Calculate the standardized test statistic.

The standardized test statistic is 1.32.

THIS IS WHAT I NEED HELP WITH PLEASE!
Determine the​ P-value.

P =

​(Round to three decimal places as​ needed.)

Answer 1

We are given
μ > 1180
α = 0.02
σ = 201.71
x = 1198.79
n = 200

The null hypothesis is μ ≤ 1180 while the alternative hypothesis is μ > 1180
The test statistic is 1.32 which means that the confidence internval is 98%. Getting the z-score
z = (x - μ) / σ
z = (1198.79 - 1180) / 201.71
z = 0.093

For a normally distributed population, the z-score of 0.093 has a p-value of
p = 0.46