4. The Pew Research Center conducted a survey in 2019 asking U.S. adults about their experiences...

4. The Pew Research Center conducted a survey in 2019 asking U.S. adults about their experiences dating online. In a random sample of 100 adults who had dated online, 25 said dating sites made them feel insecure. Research question: Is the amount of online daters who believe dating sites make them feel insecure different than a third?

a. Compute the value of the statistic.

b. What are the hypothesis statements to answer the research question?

c. Are the appropriate conditions met to conduct a hypothesis test using the standard normal distribution? Explain.

d. Compute the value of the test statistic.

e. Find p-value using the appropriate theoretical distribution in StatKey (include screenshot from StatKey): p-value =

f. What is your conclusion in the context of this study?

Expert Solution

4.

Given that,
possibile chances (x)=25
sample size(n)=100
success rate ( p )= x/n = 0.25
success probability,( po )=0.33
failure probability,( qo) = 0.67
null, Ho:p=0.33
alternate, H1: p!=0.33
level of significance, α = 0.05
from standard normal table, two tailed z α/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 proportion = p-po/sqrt(poqo/n)
zo=0.25-0.33/(sqrt(0.2211)/100)
zo =-1.7014
| zo | =1.7014
critical value
the value of |z α| at los 0.05% is 1.96
we got |zo| =1.701 & | z α | =1.96
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.70136 ) = 0.08888
hence value of p0.05 < 0.0889,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho:p=0.33
alternate, H1: p!=0.33
b.
Z test for proportion for the research question
c.
yes,
the appropriate conditions met to conduct a hypothesis test using the standard normal distribution

d.
test statistic: -1.7014
critical value: -1.96 , 1.96
e.
decision: do not reject Ho
p-value: 0.08888
f.
we do not have enough evidence to support the claim that the amount of online daters who believe dating
sites make them feel insecure different than a third.

orchestra answered 1 year ago

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