1. The following information is provided based on independent random samples tak

Question

1. The following information is provided based on independent random samples taken at two local malls to study the purchases by patrons of the two malls. WestGate EastGate Sample Size 70 85 Average Purchase $140 $146 Standard Deviation (s) $20 $24 We want to determine whether or not there is a significant difference between the average purchases by the patrons of the two malls. (16 Points) a) Formulate the null and alternative hypotheses (4 Points) b) Compute the relevant test statistic (7 Points) c) At a .05 level of significance, test the hypotheses. Interpret your result. (5 Points)

Explanation / Answer

Here, answer: a) H0: u1 = u2 against Ha: u1 is not equal to u2

i.e, u1 - u2 = 0 against Ha: u1 - u2 is not equal to 0.

Average purchases, X1 = $140

X2 = $146

Standard deviation, S1 = $20

S2 = $24

Sample size, n1 = 70

n2 = 85

Answer:b) test statistics = (x1 - x2) - (u1 - u2) ÷ under root of [(square of S1) / n1] + [(square of S2) /n2]

i.e, = ($140 - $146) - 0 / under root of [(400/70) + (576/85)]

= - 6 / under root of (5.71 + 6.78)

= - 6 / under root of 12.49

= - 6 / 3.53

= - 1.6997

Answer:c) confidence interval = ($140 - $146) +or- 0.05* under root of (5.71 + 6.78)

= ( - 21.0035, - 21.3565)

Fails to reject null hypothesis.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.