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)
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
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