Question

The New York City Department of Health and Mental Hygiene conducts regular inspections of restaurants. Each restaurant receives an inspection score, with lower scores indicating a more satisfactory inspection. Following are the scores for the most recent inspection for random samples of 25 restaurants in the boroughs of Manhattan and Queens.

Manhattan: 2, 22, 23, 0, 40, 12, 37, 43, 27, 15, 24, 8, 38, 4, 17, 21, 11, 18, 13, 30, 27, 19, 38, 21, 4

Queens: 27, 18, 14, 20, 35, 8, 42, 29, 0, 12, 25, 0, 19, 6, 13, 22, 5, 11, 0, 10, 19, 39, 2, 8, 19

Using a significance level of 0.05, can you conclude a significant difference in mean inspection scores between the two boroughs?

a. State whether the test is

i)          a two-sample t-test (independent samples)

ii)        a matched pairs

iii)       a two sample proportion test

b. Write H0 and H1

c. Using Minitab, list

• the test statistic
• the p-value
• your conclusion: reject H0 or do not reject H0. Note: if α is not provided, use a 0.05 significance level

d.   Write a sentence that explains your conclusion in context with the claim. Include the significance level and p-value in this sentence.

e.   Copy and paste the relevant Minitab output into the document. Answers alone are sufficient, you do not need to copy the exercise into the document.

Answer 1

Result:

Using a significance level of 0.05, can you conclude a significant difference in mean inspection scores between the two boroughs?

a. State whether the test is

i)          a two-sample t-test (independent samples)

b. Write H0 and H1

Ho: µ1 = µ2   H1: µ1 ≠ µ2

c. Using Minitab, list

the test statistic: 1.29

the p-value: 0.204

· your conclusion: do not reject H0.

·

· d.   Write a sentence that explains your conclusion in context with the claim. Include the significance level and p-value in this sentence.

Since the obtained p value of 0.204 is greater than the significance level 0.05,there is not enough evidence to conclude that there is difference in mean inspection scores between the boroughs of Manhattan and Queens.

e.   Copy and paste the relevant Minitab output into the document. Answers alone are sufficient, you do not need to copy the exercise into the document.

Two-Sample T-Test and CI: Manhattan:, Queens:

Method

μ₁: mean of Manhattan:

µ₂: mean of Queens:

Difference: μ₁ - µ₂

Equal variances are assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Manhattan:	25	20.6	12.4	2.5
Queens:	25	16.1	11.9	2.4

Estimation for Difference

Difference	Pooled StDev	95% CI for Difference
4.44	12.18	(-2.49, 11.37)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
1.29	48	0.204