For each of the following samples that were given an experimental treatment, tes

Question

For each of the following samples that were given an experimental treatment, test whether they represent populations that score significantly higher than the general population: (a) a sample of 100 with a mean of 82, (b)a sample of 10 with a mean of 84. The general population of individuals has a mean of 81. a standard deviation of 8, and follows a normal curve. For each sample, carry out a Z test using the five steps of hypothesis testing with a one-tailed test at the .01 significance level, and make a drawing of the distributions involved, (c) ADVANCED TOPIC: Figure the 99% confidence interval for parts (a) and (b).

Explanation / Answer

a.
Set Up Hypothesis
Null, H0: U=81
Alternate, H1: U>81
Test Statistic
Population Mean(U)=81
Given That X(Mean)=82
Standard Deviation(S.D)=8
Number (n)=100
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=82-81/(8/Sqrt(100)
Zo =1.25
| Zo | =1.25
Critical Value
The Value of |Z | at LOS 0.01% is 2.33
We got |Zo| =1.25 & | Z | =2.33
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Right Tail - Ha : ( P > 1.25 ) = 0.1056
Hence Value of P0.01 < 0.1056, Here We Do not Reject Ho

b.
Given That X(Mean)=84
Standard Deviation(S.D)=8
Number (n)=10
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=84-81/(8/Sqrt(10)
Zo =1.1859
| Zo | =1.1859
Critical Value
The Value of |Z | at LOS 0.01% is 2.33
We got |Zo| =1.1859 & | Z | =2.33
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Right Tail - Ha : ( P > 1.1859 ) = 0.1178
Hence Value of P0.01 < 0.1178, Here We Do not Reject Ho

c)
Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=82
Standard deviation( sd )=8
Sample Size(n)=100
Confidence Interval = [ 82 ± Z a/2 ( 8/ Sqrt ( 100) ) ]
= [ 82 - 2.58 * (0.8) , 82 + 2.58 * (0.8) ]
= [ 79.936,84.064 ]

ii.
Mean(x)=84
Standard deviation( sd )=8
Sample Size(n)=10
Confidence Interval = [ 84 ± Z a/2 ( 8/ Sqrt ( 10) ) ]
= [ 84 - 2.58 * (2.53) , 84 + 2.58 * (2.53) ]
= [ 77.473,90.527 ]

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.