Question

Do college students enjoy playing sports more than watching sports? A researcher randomly selected ten college students and asked them to rate playing sports and watching sports on a scale from 1 to 10 with 1 meaning they have no interest and 10 meaning they absolutely love it. The results of the study are shown below.

Playing Vs. Watching Sports

Play	2	9	1	1	3	4	7	10	6	3
Watch	1	8	1	1	5	1	7	9	2	3

Assume a Normal distribution. What can be concluded at the the αα = 0.10 level of significance level of significance?

For this study, we should use Select an answerz-test for the difference between two population proportionst-test for the difference between two dependent population meansz-test for a population proportiont-test for the difference between two independent population meanst-test for a population mean

1. The null and alternative hypotheses would be:   
2.   

H0:H0:  Select an answerp1μdμ1 ?=>≠< Select an answer0μ2p2 (please enter a decimal)   

H1:H1:  Select an answerμdμ1p1 ?<=>≠ Select an answerp20μ2 (Please enter a decimal)

2. The test statistic ?zt = (please show your answer to 3 decimal places.)
3. The p-value = (Please show your answer to 4 decimal places.)
4. The p-value is ?≤> αα
5. Based on this, we should Select an answerfail to rejectrejectaccept the null hypothesis.
6. Thus, the final conclusion is that ...
   • The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports.
   • The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population mean rating for playing sports is equal to the population mean rating for watching sports.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the ten students that were surveyed rated playing sports higher than watching sports on average.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports.

Answer 1

Given that,
mean(x)=4.6
standard deviation , s.d1=3.2387
number(n1)=10
y(mean)=3.8
standard deviation, s.d2 =3.1903
number(n2)=10
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, α = 0.1
from standard normal table,right tailed t α/2 =1.383
since our test is right-tailed
reject Ho, if to > 1.383
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =4.6-3.8/sqrt((10.48918/10)+(10.17801/10))
to =0.56
| to | =0.56
critical value
the value of |t α| with min (n1-1, n2-1) i.e 9 d.f is 1.383
we got |to| = 0.55648 & | t α | = 1.383
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value:right tail - Ha : ( p > 0.5565 ) = 0.29572
hence value of p0.1 < 0.29572,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho: u1 = u2
alternate, H1: u1 > u2
b.
test statistic: 0.56
critical value: 1.383
decision: do not reject Ho
c.
p-value: 0.29572
d.
p value is greater than alpha value
e.
we do not have enough evidence to support the claim that the population mean rating for playing sports is greater than the
population mean rating for watching sports.
h.
The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that
the population mean rating for playing sports is greater than the population mean rating for watching sports.