Answer:
The calculated value |Z| = 1.325 < 1.881 at 0.03 level of significance
Null hypothesis is accepted
Alternative hypothesis is rejected
A researcher wants to study the average miles run per day for marathon runners is 25
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 36
Given mean of the sample x⁻ = 22.8 miles
Given mean of the Population 'μ' = 25
Given standard deviation of the Population 'σ' = 10
Null hypothesis:-H₀: μ = 25
Alternative Hypothesis:H₁:μ ≠ 25
Level of significance = 3 % or 97%
The critical value Z₀.₉₇ = 1.881
Step(ii):-
Test statistic
[tex]Z = \frac{x^{-} - mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{22.8 - 25}{\frac{10}{\sqrt{36} } }[/tex]
Z = -1.325
|Z| = |-1.325| = 1.325
The calculated value |Z| = 1.325 < 1.881 at 0.03 level of significance
Null hypothesis is accepted
Alternative hypothesis is rejected
conclusion:-
A researcher wants to study the average miles run per day for marathon runners is 25
