The UMUC MiniMart sells four different types of teddy bears. The manager reports

Question

The UMUC MiniMart sells four different types of teddy bears. The manager reports that the four types are equally popular. Suppose that a sample of 500 purchases yields observed counts of 150, 125, 105, and 120 for types 1, 2, 3, and 4, respectively.

Type

1

2

3

4

Number

150

125

105

120

Assume we want to use a 0.05 significance level to test the claim that the four types are equally popular.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the P-value. Show all work; writing the correct P- value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the manager’s claim that the four types are equally popular? Justify your answer.

Type

1

2

3

4

Number

150

125

105

120

Explanation / Answer

(a) Null HYpothesis : H0 : Four types are equally popular. pi = 0.25, where i = 1,2,3,4

Alternative Hypothesis : Ha : Four types are not equally popular. pi not equal to 0.25 where i= 1,2,3,4

(b) Here we will use chi- square statistic.

THe chi- square table is given here.

so, X2 = 8.4

and here dF = 4-1 = 3 and alpha = 0.05

so X2 critical =  7.815

here, X2 > X2 critical

(c) P - value = Pr ( X2 > 8.4; 3) = 0.0384 from Chi - square table.

(d) Here alpha = 0.05 so we can reject the null hypothesis and can conclude that Four types are not equally popular.

Type Observed Number Expected Number (obs - exp)^2 (o -e)^2/e 1 150 125 625 5 2 125 125 0 0 3 105 125 400 3.2 4 120 125 25 0.2 sum 8.4

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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