PUB 504Homework #9060214 Nzeogu Emmanuel 6
PartA
9.3 (a). Testingthe hypothesis on whether the athletes in different sports vary interms of intelligent at 95% confidence interval
Basketballplayers Football players
X_{1}=460 X_{2}=442
S_{1}=92 s_{2}=57
N_{1}=102 N_{2}=117
N_{1}=102+ N_{2}=117< 120 sample size e use the ttest.
df= 217
Step1. Model: Independent random samples
Levelof measurement is intervalratio
Samplingdistribution is normal
Step2. H_{0}: µ_{1} = µ_{2}.
H_{1}: µ_{1} ≠µ_{2}
Step3. Sampling distribution = Z distribution
Alpha= 0.05, twotailed
Z(critical) = ± 1.96
Step4.
_{}= _{}
=_{}= 10.57
Z(obtained) = _{}=_{}=1.70
Step5. Z (obtained) = 1.70
Z(critical) = ± 1.96
Wecan see that both basketball players and football players averagealmost the same level of intelligence and that there is very littledifference in the sample means. The test statistic computed in step 4is a Z (obtained) of 1.70. The test statistic is not in the criticalregion, as marked by a Z (critical) score of ± 1.96 at the 0.05level, so we must fail to reject the null hypothesis of nodifference. We hence conclude that Basketball and football playershave essentially equal levels of intelligence.
9.3(b). Testingthe hypothesis on whether males and Females athletes in differentsports vary in terms of intelligent at 95% confidence interval
Males Females
X_{1}=442 X_{2}=480
S_{1}=88 s_{2}=75
N_{1}=107 N_{2}=105
Step1. Model: Independent random samples
Levelof measurement is intervalratio
Samplingdistribution is normal
Step2. H_{0}: µ_{1} = µ_{2}.
H_{1}: µ_{1} ≠µ_{2}
Step3. Sampling distribution = Z distribution
Alpha= 0.05, twotailed
Z(critical) = ± 1.96
Step4.
_{}= _{}
=11.27
Z(obtained) = _{}== 3.37
Step5. Z (obtained) = 3.37
Thetest statistic computed show that Z (obtained) of 3.37. The teststatistic is not in the critical region, as marked by a Z (critical)score of ± 1.96 at the 0.05 level, so we must fail to reject thenull hypothesis of no difference. We hence conclude that males andfemales do not have statistically significance difference inintelligent.
9.11.Testingwhether the completed course by police officers in shinbone, Kansashas increased their efficiency in clearing Crimes by arrest
H_{0}= P_{1}–P_{2}=0
Trained Untrained
P_{s1}=0.47 P_{s2}=P_{u}_{}=0.43
N_{1}=157 N_{2}=113
Step4. _{}= _{}= P_{u}=0.45
_{}=_{}
_{}=_{}=0.06
Z(obtained) = _{}=0.67
Zcritical is ±1.96
Thetest statistic computed in step 4 is a Z (obtained) of 0.67 The teststatistic is not in the critical region, as marked by a Z (critical)score of ± 1.96 at the 0.05 level, so we must fail to reject thenull hypothesis of no difference. We hence conclude that there is nosignificant difference completingcourse by police officers in shinbone Kansas and clearing Crimes byarrest.
PartB
PartC
9.1Testingthe hypothesis on whether men are significantly different s fromwomen in occupation prestige or the number of hours they work eachday at 95% confidence interval.
Therespondents were asked to state the number of hours they spent ofwork last week. The actual number of hours ranged from 1 to 89 hoursper week. The SPSS Data output below shows the group statistics ofboth gender and the number of hours spent on work per week.
RESPONDENTS SEX 
N 
Mean 
Std Deviation 
Std. Error Mean 

Hours spent on work last week 
MALE 
195 
2.68 
2.388 
.171 
FEMALE 
227 
3.21 
3.360 
.223 
Levene`s Test for Equality of Variances 
ttest for Equality of Means 

F 
Sig. 
t 
df 
Sig. (2tailed) 
Mean Difference 
Std. Error Difference 
95% Confidence Interval of the Difference 

Lower 
Upper 

HOURS SPENT ON WEEK LAST WEEK 
Equal variances assumed 
11.136 
.001 
1.837 
420 
.067 
.529 
.288 
1.096 
.037 
Equal variances not assumed 
1.884 
406.266 
.060 
.529 
.281 
1.082 
.023 
Fromthe spps data output above our df=420 and our sig(2 tail) =0.067which is greater than our standard value 0.05 hence not statisticallysignificant. The output also show our t obtained to be 1.837
Sinceour t_{(obtained)}=1.837 is less than out t critical which is 1.96 meaning that thisarea is falling beyond our critical area hence not quitestatistically significant hence we cannot reject our null hypothesis.We conclude that men are not significantly different from women inoccupation prestige.
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