Question

You may need to use the appropriate appendix table or technology to answer this question.

Consider the following hypothesis test.

H0: μ = 22

Ha: μ ≠ 22

A sample of 75 is used and the population standard deviation is 10. Compute the p-value and state your conclusion for each of the following sample results. Use α = 0.01. (Round your test statistics to two decimal places and your p-values to four decimal places.)

(a) x = 23, Find the value of the test statistic.

?

Find the p-value.

p-value = ?

State your conclusion.

a) Reject H₀. There is sufficient evidence to conclude that μ ≠ 22.

b) Do not reject H₀. There is sufficient evidence to conclude that μ ≠ 22.    

c) Reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

d) Do not reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

(b) x = 25.1, Find the value of the test statistic.

?

Find the p-value.

p-value = ?

State your conclusion.

a) Reject H₀. There is sufficient evidence to conclude that μ ≠ 22.

b) Do not reject H₀. There is sufficient evidence to conclude that μ ≠ 22.    

c) Reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

d) Do not reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

(c)

x = 20

Find the value of the test statistic.

Find the p-value.

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ ≠ 22.Do not reject H₀. There is sufficient evidence to conclude that μ ≠ 22.    Reject H₀. There is insufficient evidence to conclude that μ ≠ 22.Do not reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

Answer 1

From given data

Null hypothesis Ho :  μ =22

Alternate hypothesis Ha : μ ≠ 22 (Two tailed test)

Sample size (n)=75

Population standard deviation () = 10

Significance level () = 0.01

(a) In this

   =23

Test statistic (z) = ( - μ)/(/ n)

= (23-22)/(10/75)

=0.87

P value = 2 P(Z>0.87) = 0.3843 (From z table)

P value > significance level()

0.3843> 0.01

Opttion (d) Do not reject the null hypothesis. There is insufficient evidence to conclude that μ ≠ 22 .

(b) In this

    = 25.1

Test statistic (z) = ( - μ)/(/n)

= (25.1-22)/(10/75)

=2.68

P value = 2P(z>2.68)=0.0074 ( From z table)

P value < significance level ()

0.0074<0.01

Option(a) Reject the null hypothesis . There is sufficient evidence to conclude that  μ ≠ 22 .

(c) In this

  =20

Test statistc (z) = ( - μ)/(/n)

= ( 20-22)/(10/75)

= -1.73

P value = 2 P( z<-1.73) = 0.0836 ( From z table)

P value > significance level()

0.0836 > 0.01

Do not reject the null hypothesis. There is insufficient evidence to conclude that   μ ≠ 22 .