Answer:
We conclude that at a = 0.01, the dietician can't say that the Wonder Diet is more expensive than the Southwest Diet.
Step-by-step explanation:
We are given that Healthy Eating Magazine published the population standard deviations as $89 for the Wonder Diet and $75 for the Southwest Diet. She conducted a random sample of 20 clients on each diet. The mean amount for the Wonder Diet was $643 and the Southwest Diet was $588.
We have to test whether the Wonder Diet is more expensive than the Southwest Diet or not.
<em>Firstly, let the Population mean amount of wonder diet be </em><em />
<em>and the Population mean amount of Southwest diet be </em><em> .</em>
So, Null Hypothesis, : or {means that the Wonder Diet is less expensive than or equal to the Southwest Diet}
Alternate Hypothesis, : or {means that the Wonder Diet is more expensive than the Southwest Diet}
The test statistics that will be used here is <em><u>Two-sample z-test statistics</u></em>,i.e;
T.S. = ~ N(0,1)
where, = sample mean amount for the Wonder Diet = $643
= sample mean amount for the Southwest Diet = $588
= population standard deviation for Wonder diet = $89
= population standard deviation for Southwest diet = $75
= sample of clients for Wonder diet = 20
= sample of clients for Southwest diet = 20
So, <u>test statistics</u> =
= 2.113
<em>Now, at 0.01 significance level z table gives critical value of 2.3263. Since our test statistics is less than the critical value of z so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.</em>
Therefore, we conclude that at a = 0.01, the dietician can't say that the Wonder Diet is more expensive than the Southwest Diet.