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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.

Respuesta :

JeanaShupp

Answer: 1.9166

Step-by-step explanation:

Let [tex]\mu[/tex] be the population mean.

By considering the given description, we have

[tex]\mu=75[/tex]

n=20

[tex]\overline{x}=78[/tex]

s=7

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

Test statistic : [tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]

i.e . [tex]t=\dfrac{78-75}{\dfrac{7}{\sqrt{20}}}=1.916629695[/tex]

[tex]\approx1.9166[/tex]  [Rounded to four decimal places.]

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