Question

A brand new, local coffee shop must monitor the temperature at the coffee is brewed. Too much variation will cause inconsistent taste. Over the first 6 months of business, the standard deviation in the temperature of the water was 1.5°F. A random sample of 30 pots in the first week of business in March had a standard deviation of 2.1°F. This is a new company, which does not want to incur unnecessary costs. So before the coffee shop calls in a repairman, they want to be confident at the 99% level the standard deviation in temperature has increased above 1.5°F (indicating a faulty machine). Should the coffee shop call a repairman?

(please also specify null and alternative hypothesis)

Answer 1

H0: = 1.5

Ha: > 15

Test statistics

= ( n - 1) S² / ²

= ( 30 - 1) * 2.1² / 1.5²

= 56.84

df = n - 1 = 30 - 1 = 29

Chi-square critical value at 0.01 significance level with 29 df = 49.588

Since test statistics > 49.588, Reject h0.

We conclude at 0.01 significance level that we have sufficient evidence to support the claim

the standard deviation in temperature has increased above 1.5°F