Question

In an effort to better manage his inventory levels, the owner of two steak and seafood restaurants, both located in the same city, hires a statistician to conduct a statistical study. The owner is interested in whether the restaurant located on the south side sells more prime rib steaks per night than the restaurant located on the north side of the city.

The statistician selects a random sample of size n1 = 35 nights that the southside restaurant is open. For each night in the sample, she collects data on the number of prime rib steaks sold at the southside location and computes the sample mean x̄1 = 13.25 and the sample variance s12 = 36. Likewise, she selects a random sample of size n2 = 32 nights that the northside restaurant is open. For each night in the sample, she collects data on the number of prime rib steaks sold at the northside location and computes the sample mean x̄2 = 10.13 and the sample variance s22 = 30.

The statistician conducts an F-test of the ratio of two variances, and there is not enough evidence to infer that the population variances differ (you can assume that σ11 = σ22). Furthermore, histograms of the sample data suggest that the normality conditions are satisfied.

The point estimate of µ1 – µ2 is_____ The 90% confidence interval estimate of the difference between the mean number of prime rib steaks sold per night at the southside restaurant and the mean number of prime rib steaks sold per night at the northside restaurant is LCL =_____  to UCL = ______. The statistician formulates the null and alternative hypotheses as H0: µ1 – µ2 = 0, H:µ1 – µ2 ≠ 0 and conducts the hypothesis test at the 0.10 significance level. Since the p-value is_____, the statistician concludes that there_______enough evidence to infer that the mean nightly sales of prime rib steaks differs between the two restaurants.

Answer 1

(a)

The point estimate of µ1 – µ2 is =

(b)

Pooled SD is got as follows:

= 0.10

ndf = n1 + n2 - 2

= 35 +32 - 2

=65

From Table, critical values of t= 1.6686

LCL = 3.12 - (1.6686 X 1.4080) = 3.12 - 2.3493 = 0.77

UCL = 3.12 + (1.6686 X 1.4080) = 3.12 + 2.3493 = 5.47

So,

Answer is:

The 90% confidence interval estimate of the difference between the mean number of prime rib steaks sold per night at the southside restaurant and the mean number of prime rib steaks sold per night at the northside restaurant is LCL = 0.77 to UCL = 5.47.

(c)

By Technology,

p value = 0.0315

So,

Answer is:

The statistician formulates the null and alternative hypotheses as H0: µ1 – µ2 = 0, H:µ1 – µ2 ≠ 0 and conducts the hypothesis test at the 0.10 significance level. Since the p-value is 0.0315 the statistician concludes that there is enough evidence to infer that the mean nightly sales of prime rib steaks differs between the two restaurants.