Question

A test is made of H subscript 0 colon space mu space equals space 43 space space v e r s u s space space H subscript 1 colon space mu space greater than space 43. A sample of size n equals 76 is drawn, and the sample mean is 47. The population standard deviation is 25. Compute the value of the test statistic and determine if the H subscript 0 is rejected at the alpha equals 0.05 level.

Answer 1

The calculated value Z = 1.39 <1.96 at 0.05 level of significance

The null hypothesis is accepted

Explanation:

Step(i):-

Given that the mean of the Population = 43

Given that the mean of the sample = 47

Given that the standard deviation of the Population = 25

Given that the sample size 'n' = 76

Step(ii):-

Null hypothesis:H₀: μ = 43

Alternative Hypothesis: H₁: μ ≠ 43

Test statistic

`Z = (x^(-)-mean )/((S.D)/(√(n) ) )`

`Z = (47-43 )/((25)/(√(76) ) )`

Z = 1.39

Level of significance = 0.05

The critical value = 1.96

Final answer:-

The calculated value Z = 1.39 <1.96 at 0.05 level of significance

The null hypothesis is accepted