Question

Dr. Lilly Potter, a dietician, claims that the average number of calories in a serving of movie theater popcorn is more than 75. Ä A sample of 35 servings of popcorn was found to have an average of 78 calories with a standard deviation of 7. Use a 5% level of significance.

Answer 1

Solution :

Null and alternative hypotheses :

The null and alternative hypotheses would be as follows :

HO :μ75

H, :μ > 75

Test statistic :

To test the hypothesis the most appropriate test is one sample t-test. The test statistic is given as follows :

t= T-pl s/n

Where, x̄ is sample mean, s is sample standard deviation, n is sample size and μ is hypothesized value of population mean under H_{​​​​​​0}.

We are given the following values :

c = 78, p= 75, s= 7, n= 35

.it = (78 – 75) (7/35) - 2.5355

The value of the test statistic is 2.5355.

P-value :

Since, our test is right-tailed test, therefore we shall obtain right-tailed p-value for the test statistic. The right-tailed p-value is given as follows :

P-value = P(T > t)

P-value = P(T > 2.5355)

P-value = 0.0080

The p-value is 0.0080.

Decision :

Significance level = 0.05

P-value = 0.0080

(0.0080 < 0.05)

Since, p-value is less than the significance level of 0.05, therefore we shall reject the null hypothesis at 0.05 significance level.

Conclusion :

At 0.05 significance level, there is sufficient evidence to support the Dr. Lilly Potter's claim that the average number of calories in a serving of movie theater is more than 75.

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