7.1 normally distributed with mean ${\mu }_1-{\mu }_2$ and standard deviation $\sqrt{{\displaystyle \frac{{\sigma }_1^2}{n_1}}+{\displaystyle \frac{{\sigma }_2^2}{n_2}}}$

7.3

1. no

2. no

3. no

4. yes

5. no

7.5 b

7.7

1. 14; .4

2. 10; .3

3. 4; .5

4. yes

7.9

1. .5989

2. $t=-2.39$, reject $H_0$

3. $-1.24\pm .98$

4. confidence interval

7.11

1. reject H₀; sufficient evidence of a difference

2. fail to reject H₀; insufficient evidence of a difference

7.13

1. $({\mu }_1-{\mu }_2)$

2. $H_0:({\mu }_1-{\mu }_2)=0,H_{\text{a}}:({\mu }_1-{\mu }_2)>0$

3. yes; fail to reject $H_0$

7.15

1. $H_0:({\mu }_1-{\mu }_2)=0,H_{\text{a}}:({\mu }_1-{\mu }_2)\ne 0$

2. $t=.62$

3. $\left|t\right|>1.684$

4. fail to reject $H_0;$ supports theory

7.17

1. $(-.60,7.95)$

2. independent random samples from normal populations with equal variances

7.19

1. $t=11.87$, reject H₀

2. $t=2.94$, reject H₀

7.21 $t=.57,p\text{-value}=.573,$ fail to reject $H_0:({\mu }_1-{\mu }_2)=0$

7.23 $t=1.08$, fail to reject $H_0$

7.25

1. ${\mu }_1-{\mu }_2$

2. no

3. .2262

4. fail to reject $H_0$

7.27

1. no standard deviations reported

2. $s_1=s_2=5$

3. $s_1=s_2=6$

7.29 before

7.31 true

7.33

1. $t>1.833$

2. $t>1.328$

3. $t>2.776$

4. $t>2.896$

7.35

1. ${\bar{x}}_d=2,s_d^2=2$

2. ${\mu }_d={\mu }_1-{\mu }_2$

3. $2\pm 1.484$

4. $t=3.46,$ reject $H_0$

7.37

1. $z=1.79,$ fail to reject $H_0$

2. .0734

7.39

1. $H_0:{\mu }_d=0,H_{\text{a}}:{\mu }_d>0$

2. paired difference

3. reject $H_0$

4. $\approx 0$

5. yes

7.41

1. a. two measurements for each patient—before and after

2. c. ${\bar{x}}_d=-7.63,s_d=5.27$

3. d. $-7.63\pm 1.53$

4. e. yes; evidence that ${\mu }_{\text{before}}<{\mu }_{\text{a}}{}_{\text{fter}}$

7.43

1. ${\mu }_d$

2. paired difference

3. $H_0:{\mu }_d=0,H_{\text{a}}:{\mu }_d>0$

4. $t=2.19$

5. reject $H_0$

7.45 yes, $t=-7.34$

7.47 $t=2.92$, fail to reject $H_0$ ; no evidence of a difference

7.49

1. two scores for each twin pair

2. 95% CI for ${\mu }_d:1.95\pm 1.91$ ; control group has larger mean

7.51 $t=3.00$, reject $H_0;$ after camera mean is smaller than before camera mean

7.57 $n_1=n_2=24$

7.59

1. ${\mu }_1-{\mu }_2$

2. 1.96

3. 10

4. handshakes: 615.3; fist bumps: 36

5. 27

7.61 $n_1=n_2=49$

7.63 28

7.65 $n_1=n_2=136$

7.67 true

7.69

1. $T_1\le 41,T_1\ge 71$

2. $T_1\ge 50$

3. $T_1\le 43$

4. $\left|z\right|>1.96$

7.71 yes, $z=-2.47$

7.73

1. $T_1=62.5,\text{reject}{H}_0$

2. yes, $T_1=62.5$

7.75

1. $H_0:D_{\text{Text}}=D_{\text{NoText}},$ $H_{\text{a}}:D_{\text{Text}}>D_{\text{NoText}}$

2. reject $H_0$ ; texting group

7.77

1. rank sum test

2. $H_0:D_{\text{Low}}=D_{\text{High}},H_{\text{a}}:D_{\text{Low}}>D_{\text{High}}$

3. $T_2\le 41$

4. do not reject $H_0$

7.79

1. $H_0:D_1=D_2$

2. $z=.67$

3. $\left|z\right|>1.645$

4. fail to reject $H_0$

7.81 yes, $z=2.86$

7.83

1. $p\text{-value}=.0368$, reject $H_0$

2. $p\text{-value}=.0005$, reject $H_0$

7.85

1. data not normal

2. $z=-6.47,\text{reject}{H}_0$

3. $z=-.39,\text{do}\text{not}\text{reject}{H}_0$

4. $z=-1.35,$ $\text{do}\text{not}\text{reject}{H}_0$

7.87 data must be ranked

7.89

1. $H_{\text{a}:}{D}_{\text{A}}>D_{\text{B}}$

2. $T_{-}=3.5,\text{reject}{H}_0$

7.91

1. before and after measurements not independent

2. scores not normal

3. reject $H_0$, ichthyotherapy is effective

7.93

1. $z=-4.638$

2. yes, $p\text{-value}\approx 0$

7.95

1. a. $H_0:D_{\text{good}}=D_{\text{average}},H_{\text{a}}:D_{\text{good}}\ne D_{\text{average}}$

2. d. $T=3$

3. e. $T\le 4$

4. f. $\text{reject}{H}_0$

7.97 $T_{+}=3.5,$ reject $H_0;$ program was effective

7.99 $p-\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=.003$, reject $H_0$ ; inventory method d.

7.101 yes, $T_{-}=50.5$

7.103 independent random samples from treatment populations, or, randomly assign treatments to experimental units

7.105 True

7.107

1. plot b

2. 9; 14

3. 75; 75

4. 20; 144

5. 95 (78.95%); 219 (34.25%)

6. $\text{M}\text{S}\text{T}=75$, $\mathrm{M}\mathrm{S}\mathrm{E}=2,F=37.5;\mathrm{M}\mathrm{S}\mathrm{T}=75$, $\mathrm{M}\mathrm{S}\mathrm{E}=14.4$, $F=5.21$

7. reject $H_0;$ reject $H_0$

8. both populations normal with equal variances

9. plot a: $\text{df}(\text{T})=1$, $\text{df}(E)=10$, $\mathrm{d}\mathrm{f}(\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l})=11$, $\mathrm{S}\mathrm{S}\mathrm{T}=75$, $\mathrm{S}\mathrm{S}\mathrm{E}=20$, $(\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l})=95$, $\mathrm{M}\mathrm{S}\mathrm{T}=75$, $\mathrm{M}\mathrm{S}\mathrm{E}=2$, $F=37.5;$ plot b: $\text{df}(\text{T})=1$, $\text{df}(\text{E})=10$, $\mathrm{d}\mathrm{f}(\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l})=11$, $\text{SST}=75$, $\text{SSE}=144$, $\text{SS}(\text{Total})=219$, $\text{MST}=75$, $\text{MSE}=14.4,F=5.21$

7.109

1. b. not valid

7.111

1. completely randomized

2. college students; tanning attitude; tanned models, models with no tan, no model

3. $H_0:{\mu }_1={\mu }_2={\mu }_3$

4. variation not accounted for

5. reject $H_0$

6. independent random samples; normal populations; equal variances

7.113

1. completely randomized

2. treatments: 3, 6, 9, 12 robots; dep. variable e.: energy expanded

3. $H_0:{\mu }_3={\mu }_6={\mu }_9={\mu }_1{}_2$, $H_{\mathrm{a}}:$ At least $2\mu \text{'}\mathrm{s}$ differ

4. reject $H_0$

7.115

1. TV viewers

2. recall score

3. program rating; V, S, neutral

4. variances not taken into account

5. $F=20.45$, $p\text{-value}=.000$

6. reject $H_0$ ; mean recall scores differ among program groups

7.117 yes; $F=2026.3$

7.119

1. completely randomized; honey dosage, DM dosage, no dosage

2. $F=17.51$, $p\text{-value}=.000,$ reject $H_0:{\mu }_{\text{Honey}}={\mu }_{\text{D}}{}_{\text{M}}={\mu }_{\text{C}}{}_{\text{ontrol}}$

7.121

1. a. 1132.2

2. b. 4144

3. c.

   

   Alternate View

   Source	df	SS	MS	F
   Treatment	2	1,132.2	566.10	9.97
   Error	73	4,144.0	56.77
   Total	75

4. d. yes, $F=9.97$

5. e. valid

7.123

1. $t=.78,$ fail to reject $H_0$

2. $2.5\pm 8.99$

3. $n_1=n_2=225$

7.125

1. $3.9\pm .31$

2. $z=20.60,$ reject $H_0$

3. $n_1=n_2=346$

7.127

1. yes; $T_{-}=1.5$

7.129

1. .143

2. .049

3. $z=2.27$, fail to reject $H_0$

4. reject $H_0$

7.131

1. $p\text{-value}=.871$, fail to reject $H_0:{\mu }_{\text{no}}-{\mu }_{\text{y}}{}_{\text{es}}=0$

7.133

1. time needed

2. climbers

3. paired experiment

7.135

1. $H_0:{\mu }_1={\mu }_2={\mu }_3$

2. reject $H_0$

3. ${\mu }_1$ is largest

7.137 yes; (7.43, 13.57)

7.139

1. $H_0:{\mu }_d=0,H_{\text{a}}:{\mu }_d\ne 0$

2. $z=2.08,p\text{-value}=.0376$

3. reject $H_0$

7.141

1. $t=-1.85$

7.143 $z=1.56$, fail to reject H₀

7.145

1. $.13\pm .094$

2. 83

7.147

1. use of creative ideas $(z=8.85);$ good use of job skills $(z=4.76)$