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15.07.2020 •
Mathematics
A researcher wants to study the average miles run per day for marathon runners. In testing the hypotheses: H0: μ = 25 miles vs. H1: μ ≠ 25 miles, a random sample of 36 marathon runners drawn from a normal population whose standard deviation is 10, produced a mean of 22.8 miles weekly. What is the rejection region associated with 3% significance level?
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Ответ:
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
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
Ответ: