Question

PROBLEM #1

According to last year's report, a Filipino household spends an average of 400 pesos a day for food. Suppose you recently took random samples of 30 households, and determined how much each household spent for food each day. The results revealed a mean of 390 pesos and the standard deviation of 21.50 pesos. Using 0.01 level of significance, can it be concluded that the average amount spent per day for food of a Filipino household has decreased? Assume normality over population.

Find the critical value

Answer 1

$z=\frac{400-390}{21.5/\sqrt{30}}=0.0849$

$P(z)=0.5319>0.01$

No, it hasn't decreased. Since the probability of obtaining a value of 390 with a normal distribution is 53.19%, which is greater than the significance level.