Question

Ever since Andrew took MTH 23, he has been obsessed with looking up statistics. One day, he comes across a study that claims that the amount of money a household spends on bottled water every year can be represented by a normally distributed variable ? with population mean μ =195 dollars and population standard deviation ? = 25 dollars. He can’t believe it. He checks his records and sees that last year he spent way more than that on bottled water. He decides to conduct a random sample of 13 people in his building and finds out that the average amount spent by the sample group was ?=210 dollars. Aha! Test the claim that the mean amount spent on bottled water is more than 195 dollars with a level of significance of ? =0.01. Identify the null and alternate hypotheses.

Answer 1

Solution:

Given ,

= 195

Claim: mean amount spent on bottled water is more than 195 dollars

i.e. > 195

So , the null and alternative hypothesis are

H₀ : = 195

H₁: > 195

The test statistic z is given by

z =

= (210 - 195) / (25/13)

= 2.16

Now ,  observe that ,there is > sign in H1. So , the test is right tailed.

p value = P(Z > 2.16)

= P(Z < -2.16)

= 0.0154 (use z table)

p value = 0.0154

We fail to reject the null hypothesis .

(Because the p value is greater than given  level of significance of ? =0.01.)

We can conclude that there is sufficient evidence to conclude that the mean amount spent on bottled water is more than 195 dollars