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

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=\frac{\overline{x}-\mu}{(s)/(√(n))}`

i.e .
`t=(78-75)/((7)/(√(20)))=1.916629695`

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

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