SHORT ANSWER. Write the word or phrase that best completes each statement or ans

Question

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Identify the null hypothesis and alternative hypothesis, significance level, test that will be used, P-value, test statistic, conclusion about the null hypothesis, and state the final conclusion in nontechnical terms. Note: Assume that the two samples are independent simple random samples selected from normally distributed populations.) 15) A researcher was interested in comparing the amount of time (in hours) spent watching 15) television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows. Women Men x 1-12.5 hr | x2 = 13.8 hr s1 3.9hr2 5.2hr 1-14 2 17 Use a 0.05 significance level to test the clalm that the mean amount of time spent watching television by women is smaller than the mean amount of time spent watch men. (6 POINTS

Explanation / Answer

Given that,
mean(x)=12.5
standard deviation , s.d1=3.9
number(n1)=14
y(mean)=13.8
standard deviation, s.d2 =5.2
number(n2)=17
null, Ho: u1 = u2
alternate, H1: u1 < u2
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.771
since our test is left-tailed
reject Ho, if to < -1.771
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =12.5-13.8/sqrt((15.21/14)+(27.04/17))
to =-0.7945
| to | =0.7945
critical value
the value of |t | with min (n1-1, n2-1) i.e 13 d.f is 1.771
we got |to| = 0.79454 & | t | = 1.771
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:left tail - Ha : ( p < -0.7945 ) = 0.22057
hence value of p0.05 < 0.22057,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 < u2
test statistic: -0.7945
critical value: -1.771
decision: do not reject Ho
p-value: 0.22057

we dont have evidence to say that mean amount of time spent watching television by women is smaller than mean amount of time spent watching television by men

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