Respuesta :
Answer:
We conclude that the population standard deviation is greater than 50.
Step-by-step explanation:
We are given that a sample of 16 items provides a sample standard deviation of 9.5.
Let [tex]\sigma^{2}[/tex] = population standard deviation
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma^{2} \leq[/tex] 50 {means that the population standard deviation is less than or equal to 50}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma^{2}[/tex] > 50 {means that the population standard deviation is greater than 50}
The test statistics that will be used here is One-sample chi-square test statistics;
T.S. = [tex]\frac{(n-1) \times s^{2} }{\sigma^{2} }[/tex] ~ [tex]\chi^{2}__n_-_1[/tex]
where, s = sample standard deviation = 9.5
n = sample of items = 16
So, the test statistics = [tex]\frac{(16-1) \times 9.5^{2} }{50 }[/tex] ~ [tex]\chi^{2}__1_5[/tex]
= 27.08
The value of chi-square test statistics is 27.08.
Now, at 5% level of significance the chi-square table gives a critical value of 25.00 at 15 degrees of freedom for the right-tailed test.
Since the value of our test statistics is more than the critical value of chi as 27.08 > 25.00, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the population standard deviation is greater than 50.
