Mathematics, 30.03.2020 18:42, kennieharris726

A dietician wants to know if the cost per month of the Wonder Diet is more expensive than the Southwest Diet. 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. At a = 0.01, can the dietician say that the Wonder Diet is more expensive than the Southwest Diet? Assume the populations are normally distributed.

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answered: lily3937

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.

Firstly, let the Population mean amount of wonder diet be $\mu_1$

and the Population mean amount of Southwest diet be $\mu_2$ .

So, Null Hypothesis, H_0 : $\mu_1 \leq \mu_2$ or $\mu_1 -\mu_2 \leq 0$ {means that the Wonder Diet is less expensive than or equal to the Southwest Diet}

Alternate Hypothesis, H_a : $\mu_1 \mu_2$ or $\mu_1 - \mu_20$ {means that the Wonder Diet is more expensive than the Southwest Diet}

The test statistics that will be used here is Two-sample z-test statistics,i.e;

T.S. = $\frac{(\bar X_1 -\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma^{2}_1 }{n_1}+\frac{\sigma^{2}_2}{n_2} } }$ ~ N(0,1)

where, $\bar X_1$ = sample mean amount for the Wonder Diet = $643

$\bar X_2$ = sample mean amount for the Southwest Diet = $588

$\sigma_1$ = population standard deviation for Wonder diet = $89

$\sigma_2$ = population standard deviation for Southwest diet = $75

n_1 = sample of clients for Wonder diet = 20

n_2 = sample of clients for Southwest diet = 20

So, test statistics = $\frac{(643-588)-(0)}{\sqrt{\frac{89^{2}}{20}+\frac{75^{2}}{20} } }$

= 2.113

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.

Therefore, we conclude that at a = 0.01, the dietician can't say that the Wonder Diet is more expensive than the Southwest Diet.

answered: Guest

That is right sorry i was gonna answer but i already saw his

answered: Guest

d. corresponding side lengths in similar triangles are proportional in length.

step-by-step explanation:

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A dietician wants to know if the cost per month of the Wonder Diet is more expensive than the Southw...