Answer to Question #203021 in Statistics and Probability for alcaraz

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

One sample t-test.

Null hypothesis $H_0:\mu=400.$

Alternative hypothesis $H_a:\mu<400.$

Degrees of freedom: $df=30-1=29.$

Critical t-value: $t_{crit}=-2.462.$

Test statistic: $t=\frac{390-400}{\frac{21.50}{\sqrt{30}}}=-2.55.$

Since the test statistic lies in the critical region, reject the null hypothesis.

There is a sufficient evidence that the average amount spent per day for food of a Filipino household has decreased.