STAT217 midterm solutions

Question 1

Ho: median £ 90

Ha: median > 90

Reject Ho if T- £ 2

Observation	1	2	3	4	5	6
| d |	45	60	60	60	90	630
Sign	-	-	+	+	+	+
Rank	1	3	3	3	5	6

T- = 1 + 3 = 4

Do not reject Ho.

Conclude the average amount of time people twitter is not significantly more than 90 minutes per week.

Question 2

Ho: s1 = s2

Ha: s1 ≠ s2

Reject Ho if F > 2.44

F = (25.96/14.58)² = 3.1703

Reject Ho.

Conclude a significant difference in the variances.

Ho: m1 £ m2

Ha: m1 > m2

d.f. = (25.96²/16 + 14.58²/25)²/[(25.96²/16)²/15 + (14.58²/25)²/24] = 21.1 => d.f. = 21

Reject Ho if t > 1.721

t = (186.47 – 125.32)/sqrt(25.96²/16 + 14.58²/25) = 8.5945

Reject Ho.

Conclude those in bedroom communities spend significantly more per month on gasoline on average.

Question 3

a) 69,402 ± 1.96(18,031)/sqrt(75)*sqrt(625/699) = 69,402 ± 3,859

65,543 < m < 73,261

b) Sample size = [700(18,031)²]/[699(1000/1.96)² + 18,031²] = 448.8 => n = 449

Question 4

a) Reject Ho if (xbar – 382,500)/[34,200/sqrt(100)] < -1.645

Reject Ho if xbar < 376,874.1

Power = P(xbar < 376,874.1 | m = 374,900)

= P(Z < 0.58) = 0.5 + 0.219 = 0.719 = 71.9%

b) 2.326 = (376,874.1 - m)/[34,200/sqrt(100)]

µ = 376,874.1 – 2.326(34,200)/sqrt(100) = 368,919.18

c) Increasing the level of significance increases the power.