Question

Problem 4: In a sample of 1000 Yuba College students, it was found that they consumed on average 23 grams of sugar with a standard deviation of 4 grams and that 230 planned to transfer to Chico State. a) (7 points) Can we conclude with 99% confidence that Yuba College students consume on average over 20 grams of sugar? Use the rejection region approach

Answer 1

In this case, we will frame our null hypothesis as

Ho : $\small \mu$ = 20gm which implies that Yuba college student consume on an average 20gm of sugar.

And alternative hypothesis as

H1 :  $\small \mu$ > 20gm which implies that average sugar consumed by Yuba college students is over 20gm.

Test statistic is given by z =  $\small \frac{\bar{x} - \mu}{\sigma /\sqrt{n}}$

Here sample size n is 1000

Sample mean $\small \bar{x}$ = 23

$\small \mu$ = 20 ( which is specified value of mean under Ho)

$\small \sigma$​​​​​​ = 4 ( which is standans deviation)

Putting these value in formula of test statistic we get, z = 23.81

Now at 0.01 level of significance for one tail test, critical value of standard normal variate z = 2.33

Since z statistic calculated > critical value of z, it lies in rejection region, in this case we may reject the null hypothesis. Hence, we conclude that the average sugar consumed by students of Yuba college is over 20gm.