Question

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?

Answer 1

yes, we can reject the hypothesis

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