Respuesta :
Answer:
Yes, we have enough evidence at a 0.005 level of significance to infer that the mean score for this population exceeds 73.
Step-by-step explanation:
We are given that a random sample of 10 scores on a recent chemistry exam is given below:
83, 81, 85, 87, 79, 73, 84, 86, 78, 84
You may take as known that the population is normal with a standard deviation of 13.
We have to conduct a hypothesis test to infer that the mean score for this population exceeds 73.
Let [tex]\mu[/tex] = mean score for this population
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 73 {means that the mean score for this population is less than or equal to 73}
Alternate Hypothesis, [tex]H_a[/tex] : [tex]\mu[/tex] > 73 {means that the mean score for this population exceeds 73}
The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean score = [tex]\frac{83+81+85+87+79+73+84+86+78+84}{10}[/tex] = [tex]\frac{820}{10}[/tex] = 82
[tex]\sigma[/tex] = population standard deviation = 13
n = sample size = 10
So, test statistics = [tex]\frac{82-73}{\frac{13}{\sqrt{10} } }[/tex]
= 2.189
So, at 0.005 level of significance, the z table gives critical value of 3.8906 for one-tailed test. Since our test statistics is less than the critical value of z so we have insufficient evidence to reject null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean score for this population exceeds 73.
