Question

In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7. Compute the z or t value of the sample test statistic.

Answer 1

Answer: 1.9166

Step-by-step explanation:

Let $\mu$ be the population mean.

By considering the given description, we have

$\mu=75$

n=20

$\overline{x}=78$

s=7

Since, the population standard deviation is  unknown , so we use t-test.

Test statistic : $t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

i.e . $t=\dfrac{78-75}{\dfrac{7}{\sqrt{20}}}=1.916629695$

$\approx1.9166$  [Rounded to four decimal places.]

Hence, the value of the t-test statistic : 1.9166