Question

In an effort to better manage her 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 east side sells more prime rib steaks per night than the restaurant located on the west side of the city. The statistician selects a random sample of size 48 nights that the eastside restaurant is open. For each night in the sample, he collects data on the number of prime rib steaks sold at the eastside location and computes the sample mean μ₁ = 18.43 and the sample variance σ₁² = 22. Likewise, he selects a random sample of size 41 nights that the westside restaurant is open. For each night in the sample, he collects data on the number of prime rib steaks sold at the westside location and computes the sample mean μ₂ = 14.11 and the sample variance σ₂² = 52. The statistician conducts an F-test of the ratio of the two variances and finds that there is not enough evidence to infer that the population variances differ (assuming σ₁² = σ₂²). Furthermore, histograms of the sample data suggest that the normality conditions are satisfied. The point estimate of σ₁²/σ₂² is unknown. The 95% confidence interval estimate of the difference between the mean number of prime rib steaks sold per night at the eastside restaurant and the mean number of prime rib steaks sold per night at the westside restaurant is LCL = -0.0234 and UCL = 0.0063. The statistician formulates the null and alternative hypotheses as Ho: μ₁ - μ₂ = 0 and Ha: μ₁ - μ₂ ≠ 0 and conducts the hypothesis test. The statistician concludes that there is enough evidence to infer that the mean nightly sales of prime rib steaks differs between the two restaurants (p-value = 0.0001).

In an effort to better manage her 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 east side sells more prime rib steaks per night than the restaurant located on the west side of the city.

The statistician selects a random sample of size 48 nights that the eastside restaurant is open. For each night in the sample, he collects data on the number of prime rib steaks sold at the eastside location and computes the sample mean μ₁ = 18.43 and the sample variance σ₁² = 22. Likewise, he selects a random sample of size 41 nights that the westside restaurant is open. For each night in the sample, he collects data on the number of prime rib steaks sold at the westside location and computes the sample mean μ₂ = 14.11 and the sample variance σ₂² = 52.

The statistician conducts an F-test of the ratio of the two variances and finds that there is not enough evidence to infer that the population variances differ (assuming σ₁² = σ₂²). Furthermore, histograms of the sample data suggest that the normality conditions are satisfied.

The point estimate of σ₁²/σ₂² is unknown.

The 95% confidence interval estimate of the difference between the mean number of prime rib steaks sold per night at the eastside restaurant and the mean number of prime rib steaks sold per night at the westside restaurant is LCL = -0.0234 and UCL = 0.0063.

The statistician formulates the null and alternative hypotheses as Ho: μ₁ - μ₂ = 0 and Ha: μ₁ - μ₂ ≠ 0 and conducts the hypothesis test. The statistician concludes that there is enough evidence to infer that the mean nightly sales of prime rib steaks differs between the two restaurants (p-value = 0.0001).

Added by Jennifer W.

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