Hypothesis Test of 2 Means A researcher wants to test the claim that, on average

Question

Hypothesis Test of 2 Means A researcher wants to test the claim that, on average, more juveniles than adults are classi- fied as missing persons. Records for the last 5 years were recorded as follows: Juveniles: 65513 65934 64213 61914 59167 Adults: 31364 34478 36937 35946 38209 2. Test the claim at 0.05 level of significance. Test statistic t State the null and alternative hypothesis. State your conclusion for your hypothesis test. 4 points 4 points Hypothesis Test of 1 Proportion 3. A new insectercide is advertized to kill more than 95% of roaches on contact. The insectercide was applied to 400 roaches. Only 384 died immediately after contact. a. Is this sufficient evidence to support ther manufacturer's claim of 95%. Use = 0.05 Level of significance. Find a 95% confidence interval for the true proportion ofroaches killed on contact. b Test statistic Z-p-Po= and Confidence Interval ±Zg.pa State the null and alternative hypothesis 4 points State your conclusion for your hypothesis test. 4 points 4 Give the 95% Confidence Interval Give a conclusion for the confidence interval test. 4 points rsons

Explanation / Answer

Q3.

PART A.
Given that,
possibile chances (x)=384
sample size(n)=400
success rate ( p )= x/n = 0.96
success probability,( po )=0.95
failure probability,( qo) = 0.05
null, Ho:p=0.95  
alternate, H1: p>0.95
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.96-0.95/(sqrt(0.0475)/400)
zo =0.9177
| zo | =0.9177
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =0.918 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: right tail - Ha : ( p > 0.91766 ) = 0.1794
hence value of p0.05 < 0.1794,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.95
alternate, H1: p>0.95
test statistic: 0.9177
critical value: 1.64
decision: do not reject Ho
p-value: 0.1794

PART B.
TRADITIONAL METHOD
given that,
possibile chances (x)=384
sample size(n)=400
success rate ( p )= x/n = 0.96
I.
sample proportion = 0.96
standard error = Sqrt ( (0.96*0.04) /400) )
= 0.0098
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
margin of error = 1.96 * 0.0098
= 0.0192
III.
CI = [ p ± margin of error ]
confidence interval = [0.96 ± 0.0192]
= [ 0.9408 , 0.9792]
-----------------------------------------------------------------------------------------------
DIRECT METHOD
given that,
possibile chances (x)=384
sample size(n)=400
success rate ( p )= x/n = 0.96
CI = confidence interval
confidence interval = [ 0.96 ± 1.96 * Sqrt ( (0.96*0.04) /400) ) ]
= [0.96 - 1.96 * Sqrt ( (0.96*0.04) /400) , 0.96 + 1.96 * Sqrt ( (0.96*0.04) /400) ]
= [0.9408 , 0.9792]
-----------------------------------------------------------------------------------------------
interpretations:
1. We are 95% sure that the interval [ 0.9408 , 0.9792] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

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