A fast-food restaurant claims that a small order of french fries contains 120 calories. A nutritionist is concerned that the tru

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2 months ago

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A fast-food restaurant claims that a small order of french fries contains 120 calories. A nutritionist is concerned that the tru

e average calorie count is higher than that. The nutritionist randomly selects 35 small orders of french fries and determines their calories. The resulting sample mean is 155.6 calories, and the p-value for the hypothesis test is 0.00093. Which of the following is a correct interpretation of the p-value?
a. If the population mean is 120 calories, the p -value of 0.00093 is the probability of observing a sample mean of 155.6 calories or less.
b. If the population mean is 120 calories, the p-value of 0.00093 is the probability of observing a sample mean of 155.6 calories or more, or a sample mean of 84.4 calories or less.
c. If the population mean is 155.6 calories, the p-value of 0.00093 is the probability of observing a sample mean of 120 calories or more.
d. If the population mean is 155.6 calories, the p-value of 0.00093 is the probability of observing a sample mean of 120 calories or less.

Mathematics

1 answer:

tester [12.3K] · Answer 1 · 2026-02-17T20:10:14+03:00

Answer:

The correct choice is (C).

Step-by-step explanation:

The p-value is defined as the probability, under the null hypothesis (H₀), of obtaining a result that is equal to or greater than the actual observed result in a statistical hypothesis test.

A small p-value (usually ≤ 0.05) indicates strong evidence against the null hypothesis (H₀), resulting in its rejection.

A larger p-value (> 0.05) indicates weak evidence against H₀, which leads to failure in rejecting the null hypothesis.

A nutritionist has concerns that the actual average calorie content of the french fries served at a fast-food restaurant exceeds 120 calories.

The testable hypothesis can be stated as:

H₀: The actual average calorie count in the french fries is 120 calories, meaning μ = 120.

Hₐ: The average calorie count in the french fries exceeds 120 calories, meaning μ > 120.

The statistical test is as follows:

$z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}$

The average calorie count among the 35 sampled small orders of fries is:

$\bar x=155.6$

Consequently, the p-value is:

p-value = 0.00093

<pthis>p-value represents the probability of achieving a sample mean of 155.6 calories or higher when the population mean is 120 calories.

In summary,

$\bar x-\mu=155.6-120=35.6$

The interpretation of the p-value can also include the probability of observing a mean of 84.4 calories or less when the population mean is established at 120 calories.

$\bar x-\mu=-35.6$ *

*Given the symmetry of the normal distribution, P(Z < -z) = P(Z > z).

Thus,

$\bar x-\mu=-35.6$

$\\\bar x=-35.6+120\\\bar x=84.4$

Therefore, the appropriate choice is (C).

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