Question

You wish to test the following claim (H1H1) at a significance level of α=0.10α=0.10.

      Ho:μ=81.4Ho:μ=81.4
      H1:μ≠81.4H1:μ≠81.4

You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

data
83.3
77.1
85.9
86.3
77.6
79
88.4
81.3
89

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±±

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

• in the critical region
• not in the critical region

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 81.4.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 81.4.
• The sample data support the claim that the population mean is not equal to 81.4.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 81.4.

Answer 1

Solution:- Given that 83.3,77.1,85.9,86.3,77.6,79,88.4,81.3,89

=> μ = 81.4 , X = 83.1, s = 4.5733, n = 10, df = 9

=> Critical value = +/- 1.833

=> test statistic = (83.1-81.4)/(4.5733/sqrt(10)) = 1.175

=> The test statistic is in the critical region.

=> option A.
This test statistic leads to a decision to reject the null

=> option B.

test statistic = (X- mean)/(s/sqrt(n))