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Consider the following problem: The box fill weight of Frosted Flakes breakfast cereal follows a normal distribution with a mean of 9.75 ounces and a standard deviation of 0.27 ounces. A sample of 25 boxes filled this morning showed a mean of 9.85 ounces. At the 0.05 significance level, can we conclude that the mean weight is more than 9.75 ounces per box

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Answer:

Yes, we can

Step-by-step explanation:

H0 : μ = 9.75

H1 : μ > 9.75

n = 25 ; xbar = 9.85 ; σ = 0.27

The test statistic:

T = (xbar - μ) ÷ (σ / √n)

T = (9.85 -9.75) ÷ (0.27 ÷ √25)

T = 0.1 ÷ 0.054

T = 1.85

We can obtain the Pvalue from the test statistic using the Pvalue calculator :

Pvalue at t score = 1.85 ; 24 = 0.038

If Pvalue < α ; Reject H0

α = 0.05

Since Pvalue < α ; We reject H0 and conclude that mean weight is more than 9.75 ounces per box

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