A recent survey was conducted with a simple random sample of 35 shoppers at the food court in a local mall. The mall claims that the mean price for lunch is less than $4.65. The mean of the sample is $4.49, and the standard deviation of the population of lunch shoppers is $0.36. A P-value of 0.0043 is found using a 0.01 significance level to test the claim that the mean price for lunch is less than $4.65. State the conclusion about the null hypothesis.

Question

Mathematics

Korbin George

23 January, 19:04

A recent survey was conducted with a simple random sample of 35 shoppers at the food court in a local mall. The mall claims that the mean price for lunch is less than $4.65. The mean of the sample is $4.49, and the standard deviation of the population of lunch shoppers is $0.36. A P-value of 0.0043 is found using a 0.01 significance level to test the claim that the mean price for lunch is less than $4.65. State the conclusion about the null hypothesis.

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Rodrigo Taylor · Answer 1

There is enough confidence to reject the claim that the mean price is less than $ 4.65

Step-by-step explanation:

Claim: The mean price for lunch is less than $4.65

The Null hypothesis will be: The mean price for lunch is equal to or greater than $ 4.65

Let u represents the mean price of lunch, the null and alternate hypothesis can be written as:

Null Hypothesis: u ≥ 4.65

Alternate Hypothesis: u < 4.65

Calculated p-value = 0.0043

Significance Level = α = 0.01

Since the p value is less than the significance level, we can reject the claim that the mean price if less than $ 4.65

Conclusion: There is enough confidence to reject the claim that the mean price is less than $ 4.65