Homework 8 Solutions

 

Section 7.1

 

Page 374, #10

 

Model A

Model B

n = 34

n = 46

s = 10

s = 18

 

(a)     H0: m1 = m2

Ha: m1 ¹ m2

 

(b)     z0 = 2.575                        Rejection region: z > 2.575, z < -2.575

 

 


(c)          

 

 

 

(d)    Reject H0.  The mean repair costs are not the same.

 

 

Page 374, #12

 

College Prep

General

n = 49

n = 44

s = 4.8

s = 5.4

 

 

(a)                 H0: m1 - m2 ≤ 0

Ha: m1 - m2  > 0       (claim)

 

(b)           z0 = 1.285                                Rejection region: z > 1.285

 

(c)          

(d)           Reject the null hypothesis.  You can support the claim made by the guidance counselor.

 

 

Page 377, #22

 

H0: m2 - m1 ≤ $20,500                                              [Alternate form:    H0: m1 - m2 ≥ -$20,500

Ha: m2 - m1  > $20,500 (claim)                                                                Ha: m1 - m2  < -$20,500 (claim)

                                                                                                                Then conduct test accordingly for same result]

 

z0 = 1.64                  Rejection region: z > 1.645

 

Do not reject H0.  There is not enough evidence to support the claim.

 

Page 377, #24

 

 

95% CI:    

 

Page 378, #26

 

H0: mA - mB ≤ 0

Ha: mA - mB  > 0      (claim)

 

z0 = 1.645                                Rejection region: z > 1.645

 

 

Reject H0.  Would recommend Irinotecan to give pain relief longer.  Enough evidence to support the claim.

 

 

Section 8.2

 

Page 385, #10

 

H0: m1 - m2 ≤  0       (claim)

Ha: m1 - m2  > 0      

 

(a)          

 

(b)          

 

(c)           tc = 2.65                  Reject H0 if t > 2.65

               

                The standardized test statistics, t, is not in the rejection region.  Fail to reject H0. 

 

(d)           Not enough evidence to reject the claim.

 

 

Page 385, #14

 

(a)           H0: m1 ≤ m2

Ha: m1 > m2

 

(b)            tc = 1.363                              Reject H0 if t > 1.363

 

(c)          

 

(d)           Reject H0.  There is enough evidence to conclude that the mean bumper repair cost is more for small pickups than for small utility vehicles.

Page 388, #22

 

Degrees of freedom = n1 + n2 – 2 = 15 + 12 – 2 = 25

tc = 2.060

 

90% CI: 

 

 

Page 388, #24

 

Arby’s

McD’s

n = 15

n = 12

s = 2.42

s = 1.65

 

 

90% CI: 

 

Degrees of freedom: 12 – 1 = 11 (assuming unequal variances)

 

tc = 1.796

 

 

 

Section 8.3

 

Page 396, #16

 

(a)           H0:  md ≥ 0

                Ha:  md < 0               (claim)

 

(b)           t0 = -3.143               Reject H0 if t < -3.143

 

(c)          

 

(d)          

 

(e)           Reject H0.  There is enough evidence to support the claim.

 

 

 

 

Page 398, #20

 

(a)           H0:  md ≤ 0

                Ha:  md > 0               (claim)

 

(b)           t0 = 1.833                Reject H0 if t > 1.833

 

(c)          

 

(d)          

 

(e)           Reject H0.  There is enough evidence to support the claim.

 

 

Page 399, #24

 

                                t0 = 2.262               

               

 

               

 

 

Section 8.4

 

Page 405, #10

 

CA: 18.4% of 1500 is 276

OR: 20.7% of 1000 is 207

 

 

 

(a)           H0:  p1 ≥ p2

                Ha:  p1 < p2             (claim)

 

(b)           z0 = -1.645              Reject H0 if z < -1.645

 

(c)          

(d)           Fail to reject H0.  There is not enough evidence to support the claim that the proportion of adult smokers in CA is less than in OR.

 

 

 

Page 406, #14

 

H0:  pS ≤ pW

Ha:  pS > pW                  (claim)

 

z0 = 2.325                Reject H0 if z > 2.325

 

 

 

 

Reject H0.  There is enough evidence to support the claim.

 

 

Page 406, #18

 

 

 

 

 


95% CI: