AT&T; TE 9:30 PM ecourses.pvamu.edu TOBLEMS 1 of 3 b. What if the research quest

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AT&T; TE 9:30 PM ecourses.pvamu.edu TOBLEMS 1 of 3 b. What if the research question were changed to 8.1 a. For each situation, find Z(critical). "Do seniors cut a significantly greater number of classes How would the test conducted in prob- Alpha (a) Form of the test lem 8.2a change? (HIN This wonding implies 005 one-tailed test of significance How would the research hypothesis change? For the alpha you 006 ased in problem &2a, what would the value of 00 Z critical) be? 83 a. Statewide, social workers average 10.2 years of experience. random sample, 203 social In a For each situation, find the critical t score. workers in greater metropolitan Shinbone aver age only 87 years, with a standard deviation of Form of the 0.52. Are social workers in Shinbone signifi- Alpha (o) cantly less experienced? (NOTE: The wording the research hypothesis may jastify one-tailed 0.02 test of significance. For a one-tailed test, what 0.0 121 form would the research hypothesis take, and 0.0 31 where would the critical region begin? 005 61 The same sample of social workers reports an average annual salary of S25,782, with a stan- Compute the appropriate test statistic GZ or for dard deviation of S622.ls this figure significantly each situation. higher than the statewide average of S24,509? (NOTE: The wording of the research hypothesis suggests a one-tailed test. What forma would the or t( research hypothesis take, and where would the X- 220 critical region begin) 0.75 8A SOC statewide, the average score on the verbal por- 17.1 6.8 s 09 tion of the college entrance exam is 453, with a stan- dard deviation of 95. A random sample of 137 seniors 102 X 94 Littlewood Regional High School shows a mean score of 502. les there a significant difference? 8s SOC A random sample of 423 chinese Americans 0.57 0.60 drawn from the population of a particular state has 0.32 P. 030 finished an average of 127 years of formal education, with a standard deviation of 1.7. ls this significantly different from the statewide average of 122 years? &2 a. SoC The students at Littlewood Regional High 86 SOCAsampleofIossanitation workers for the city School cut an average of 33 classes per month. A random sample of 117 seniors averages 38 Euonymus, Texas, earns an average of S24.375 cuts per month, with a standard deviation of per year. The average salary for all Euony mus city 0.53. Are seniors significantly different from the workers is $24,230, with a standard deviation of student body as a whole? (HINT: The wording SS23. Are the sanitation workers overpaid? Conduct of the research question suggests a two-tailed both one- and two-tailed tests. test. This means that the alternative, 87 a. Soc suwewide, he population as a whole watches hypothesis in step 2 will be stated as HER 33 62 hours TV per day.Arandom sample of 1017 and that the critical region will be split between senior citizens in the state report watching an aver- the upper and lower aails the sampling distri- age of 5.9 hours per day, with a standard deviation bution. See Table &3 for values of zcritical for of 07 the difference significant various alpha levels) 78%

Explanation / Answer

Q 8.2.
a.
Given that,
population mean(u)=3.3
standard deviation, =0.53
sample mean, x =3.8
number (n)=117
null, Ho: =3.3
alternate, H1: !=3.3
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 3.8-3.3/(0.53/sqrt(117)
zo = 10.20439
| zo | = 10.20439
critical value
the value of |z | at los 5% is 1.96
we got |zo| =10.20439 & | z | = 1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 10.20439 ) = 0
hence value of p0.05 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: =3.3
alternate, H1: !=3.3
test statistic: 10.20439
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0

b.
Given that,
population mean(u)=3.3
standard deviation, =0.53
sample mean, x =3.8
number (n)=117
null, Ho: =3.3
alternate, H1: >3.3
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 3.8-3.3/(0.53/sqrt(117)
zo = 10.20439
| zo | = 10.20439
critical value
the value of |z | at los 5% is 1.645
we got |zo| =10.20439 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : right tail - ha : ( p > 10.20439 ) = 0
hence value of p0.05 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: <3.3
alternate, H1: >3.3
test statistic: 10.20439
critical value: 1.645
decision: reject Ho
p-value: 0

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