Question

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?

Answer 1

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

           $Z = \frac{x^{-} - mean}{\frac{S.D}{\sqrt{n} } }$

          $Z = \frac{22.8 - 25}{\frac{10}{\sqrt{36} } }$

          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