Follow the 6-step Hypothesis Testing Method for both problems. Show All work for
ID: 3222239 • Letter: F
Question
Follow the 6-step Hypothesis Testing Method for both problems. Show All work for each step!
1) Assume that the samples are independent and that they have been randomly selected. A researcher finds that of 1000 people who said that they attend a religious service at least once a month, 31 stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.10 significance level, test the claim that the two proportions are equal.
2) Assume that the samples are independent and that they have been randomly selected. Do not assume that the population standard deviations are equal. Two types of flares are tested and their burning times (in minutes) are recorded. The summary statistics are given below. Test the claim that the mean burn time for Brand X is greater than the mean burn time for Brand Y using a significance level of 0.02.
BRAND X BRAND Y n1 = 35 n2 = 40 xbar1 = 19.4 min xbar2 = 15.1 min s1 = 1.4 min s2 = 0.8 minExplanation / Answer
Q1.
Given that,
sample one, x1 =31, n1 =1000, p1= x1/n1=0.031
sample two, x2 =22, n2 =1200, p2= x2/n2=0.018
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, = 0.1
from standard normal table, two tailed z /2 =
since our test is two-tailed
reject Ho, if zo < -1.645 OR if zo > 1.645
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.031-0.018)/sqrt((0.024*0.976(1/1000+1/1200))
zo =1.929
| zo | =1.929
critical value
the value of |z | at los 0.1% is 1.645
we got |zo| =1.929 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.9293 ) = 0.0537
hence value of p0.1 > 0.0537,here we reject Ho
ANSWERS
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null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: 1.929
critical value: -1.645 , 1.645
decision: reject Ho
p-value: 0.0537
both proportions are not equal