It is believed that the average amount of money spent per U. S. household per week on food is about $98, with standard deviation $10. A random sample of 100 households in a certain affluent community yields a mean weekly food budget of $100. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average. Are the results significant at the 5% level?

Question

Makena Sanders

Mathematics

12 September, 15:10

It is believed that the average amount of money spent per U. S. household per week on food is about $98, with standard deviation $10. A random sample of 100 households in a certain affluent community yields a mean weekly food budget of $100. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average. Are the results significant at the 5% level?

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Anastasia Stokes · Answer 1

yes, we can reject the hypothesis

Step-by-step explanation:

The null hypothesis

H0 = mean weekly food budget for all households in this community is $98

Let's find z

z = (x - mean) / standard deviation / √sample size

z = (100 - 98) / 10 / √100

z = 2

Using a Z table we can find probability

P (z>2) = 0.0228

Since P < α, results are significant and we can reject the hypothesis