Question

Consider the following hypothesis test.

H₀: μ = 15

H_a: μ ≠ 15

A sample of 50 provided a sample mean of 14.07. The population standard deviation is 3.

(a)

Find the value of the test statistic. (Round your answer to two decimal places.)

(b)

Find the p-value. (Round your answer to four decimal places.)

p-value =

(c)

At

α = 0.05,

state your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ ≠ 15.Reject H₀. There is insufficient evidence to conclude that μ ≠ 15.     Do not reject H₀. There is sufficient evidence to conclude that μ ≠ 15.Do not reject H₀. There is insufficient evidence to conclude that μ ≠ 15.

(d)

State the critical values for the rejection rule. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ ≠ 15.Reject H₀. There is insufficient evidence to conclude that μ ≠ 15.     Do not reject H₀. There is sufficient evidence to conclude that μ ≠ 15.Do not reject H₀. There is insufficient evidence to conclude that μ ≠ 15.

Answer 1

Answer)

Ho : u = 15

Ha : u is not equal to 15

This is a two tailed test

N (sample size) = 50

Sample mean = 14.07

Population standard deviation = 3

As the population standard deviation is known here, we can use z test

A)

Test statistics z = (sample mean-claimed mean)/(s.d/√n)

= (14.07-15)/(3/√50)

= -2.19

B)

From z table, p(z<-2.19) = 0.0143

But this is for one tail

And our test is two tailed

And as the standard normal z table is symmetrical

Therefore, our p-value would be

2*0.0143 = 0.0286

P-value = 0.0286

Given significance level alpha = 0.05

And obtained p-value is less than 0.05

Therefore, we reject the null hypothesis

There is sufficient evidence to conclude that u is not equal to 15