A matched pairs experiment compares the taste of instant versus fresh-brewed cof

Question

A matched pairs experiment compares the taste of instant versus fresh-brewed coffee. Each object tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 40 subjects who participate in the study. 12 prefer the instant coffee, let p be the probability that a randomly chosen subject prefers fresh-brewed coffee to Instant coffee, (in practical terms, p is the proportion of the population who prefer fresh-brewed coffee.) a. How many in the sample prefer fresh-brewed coffee? b. We wish to test the claim that a majority of people prefer the taste of fresh -brewed coffee. i. Provide the null and alternative hypotheses. ii. Check the necessary assumptions. ii. Calculate the test statistic. iv. Compute the p-value. v. Draw and Write a conclusion. You are planning an evaluation of a semester-long alcohol awareness campaign at your college. Previous evaluations indicate that about 25% respond "Yes" to the question "Did the campaign alter your behavior toward alcohol consumption? How large a sample of students should you take If you want the margin of error for a 95% confidence interval to be about 0.1? A researcher conducted a study that examined the proportion of high school students who cheated on tests at least twice during the past year. Included in that study were the results for both 2002 and 2004. A reported 9054 out of 24, 142 students said they cheated at least twice in 2004. A reported 5784 out of 12, 121 students said they cheated at least twice in 2002. a. Provide an estimate for the difference between these two proportions. b. Provide a 90% confidence interval for the difference between these two proportions.

Explanation / Answer

Q3.

Given that,
no.of fresh brewed coffee (x)= 40 - 12 = 28
sample size(n)=40
success rate ( p )= x/n = 0.7
success probability,( po )=0.5
failure probability,( qo) = 0.5
null, Ho:p=0.5
alternate, H1: p>0.5
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=0.7-0.5/(sqrt(0.25)/40)
zo =2.5298
| zo | =2.5298
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =2.53 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 2.52982 ) = 0.00571
hence value of p0.05 > 0.00571,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.5
alternate, H1: p>0.5
test statistic: 2.5298
critical value: 1.64
decision: reject Ho
p-value: 0.00571

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