Find the p value and whether or not the null hypothesis will be rejected at a significance level of 0.5 (see description)

Question

A. H₀: µ≤60

H1:µ>60

Test statistic of 2.35

B. H₀: µ≥42

H₁: µ<42

Test statistic of -1.13

C. H₀: µ=88

H₁: µ≠88

Answer 1

Hi Ann,

Great question! I am certain that several others taking statistics courses are working on very similar problems as this is one of the most important concepts in statistics.

Case A: H0: u <= 60 vs H1: u > 60

1. Test Statistic: 2.35
2. p-value: 0.0094
3. Reject Null Hypothesis at alpha = 0.05: Yes

Case B: H0: u >= 42 vs H1: u < 42

1. Test Statistic: -1.13
2. p-value: 0.1292
3. Reject Null Hypothesis at alpha = 0.05: No

Case C: H0: u = 88 vs H1: u not equal to 88

1. Test Statistic: Not provided
2. p-value: Not calculated
3. Reject Null Hypothesis at alpha = 0.05: Cannot determine

Interpretation:

1. In Case A, the p-value is less than the significance level alpha = 0.05, so we reject the null hypothesis. This suggests there is evidence to support that u is greater than 60.
2. In Case B, the p-value is greater than alpha, so we do not reject the null hypothesis. This suggests there is not enough evidence to support that u is less than 42.
3. In Case C, we cannot determine the outcome because the test statistic is not provided.

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Best regards,

Ben