Answer:
Step-by-step explanation:
Hello!
Interest hypothesizes is that the variance of the golfer's scores equals to δ²= 10.0.
A random sample of 28 rounds of golf had a sample standard deviation S= 3.5
The statistics hypotheses are:
H₀: δ²= 10.0
H₁: δ²≠ 10.0
α: 0.05
To conduct a hypothesis test for the population variance you have to work using the Chi-Square distribution, this test is two-tailed so you will have two critical values. Between these two values is defined as the "not rejection region" and below and above them lies the "rejection region"
Lower critical value: [tex]X^2_{n-1; \alpha /2}= X^2_{27; 0.05}= 16.928[/tex]
Upper critical value: [tex]X^2_{n-1;1-\alpha /2}= X^2_{27;0.95}= 40.113[/tex]
If [tex]X^2_{H_0}[/tex] ≤ 16.928 or [tex]X^2_{H_0}[/tex] ≥ 40.113, the decision is to reject the null hypothesis.
If 16.928 < [tex]X^2_{H_0}[/tex] < 40.113, the decision is to not reject the null hypothesis.
[tex]X^2= \frac{(n-1)S^2}{Sigma^2} ~~X^2_{n-1}[/tex]
[tex]X^2_{H_0}= \frac{(28-1)12.25}{10} = 33.075[/tex]
The calculated [tex]X^2_{H_0}[/tex] is between the two critical values, so the decision is to not reject the null hypothesis. We can conclude that the population variance fro this golfers play score is 10.
I hope this helps!
The test statistic is 33.08 and it can be deduced that we fail to reject the null hypothesis.
It should be noted that test statistic simply means a number that's calculated from a statistical test of hypothesis.
From the information given, the test statistic will be calculated thus:
= [(28 - 1) × 3.5²/10
= (27 × 3.5²)/10
= 33.08
The lower critical value is 16.151 and the higher critical value is 40.113.
Based on the above, we fail to reject the null hypothesis and can't conclude that the variance for the golfer's score isn't equal to 10.0.
Learn more about test statistic on:
https://brainly.com/question/15980493
