Question

A test of sobriety involves measuring the subject's motor skills. A sample of 31 randomly selected sober subjects take the test and produce a mean score of 64.4 with a standard deviation of 2. A claim is made that the true mean score for all sober subjects is equal to 65. For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t =" before your answers. Round each of your answers to 3 places after the decimal point.

(a) Calculate the value of the test statistic used in this test. Test statistic's value =

(b) Use your calculator to find the P-value of this test. P-value =

(c) Use your calculator to find the critical value(s) used to test this claim at the 0.2 significance level. If there are two critical values, then list them both with a comma between them. Critical value(s) =

Answer 1

We have given Sample size = 31

Sample mean xbar = 64.4

Sample standard deviation s= 2

Here population standard deviation is not known 30 so we will use one sample t test.

The hypotheses are

H₀: μ= 65

H_a: μ ≠ 65

This is two-sided test.

1. Test statistics:

Test statistics value (t) = (xbar – μ) / (s/√n) = (64.4 - 65)/(2/sqrt(31)) = -1.670

Test statistics value (t) = -1.670

2. P value = T.DIST.2T(-1.670,30)= 0.1053….. (using Excel)

P value = 0.1053

3. Sine significant level (α) = 0.2 To find two tailed critical value, α/2 = 0.1   t-critical values = =T.INV(0.1,30) = -1.31, 1.31

Decision: Reject H₀ because the P- value is less than the significant level 0.2 so reject null hypothesis at 0.2 level of significant.

Using critical value approach, |t| = 1.67 > 1.31 so reject null hypothesis.

Conclusion: At 2% level of significance, there is sufficient evidence to conclude the claim that true mean score for all sober subject is different from 65.