Question

Which of the following statements is false?

		When the alternative hypothesis is two-sided, any hypothesis test is said to be a two-tailed test
		When the alternative hypothesis is two-sided, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic’s sampling distribution
		When the alternative hypothesis is two-sided, the rejection region is split between the two tails of the test statistic’s sampling distribution
		None of the above

A social worker was interested in determining whether there is a significance difference in the average monthly cost per child for childcare outside the home between state supported facilities and privately owned facilities. Two independent random samples yielded the following information:

	State Supported Facilities (population 1)	Privately Owned Facilities (population 2)
Sample Size	64	64
Sample Mean	705	675
Standard Deviation	95	80

Which Excel will calculate the test statistic?

	a.	=(705-675)/(SQRT(95/64+80/64))
	b.	=(705-675)/(SQRT(95^2/8+80^2/8))
	c.	=(705-675)/(SQRT(95/8+80/8))
	d.	=(705-675)/(SQRT(95^2/64+80^2/64))

Answer 1

Given that,
mean(x)=705
standard deviation , s.d1=95
number(n1)=64
y(mean)=675
standard deviation, s.d2 =80
number(n2)=64
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =1.998
since our test is two-tailed
reject Ho, if to < -1.998 OR if to > 1.998
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =705-675/sqrt((9025/64)+(6400/64))
to =1.932
| to | =1.932
critical value
the value of |t α| with min (n1-1, n2-1) i.e 63 d.f is 1.998
we got |to| = 1.93241 & | t α | = 1.998
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.9324 ) = 0.058
hence value of p0.05 < 0.058,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 1.932
critical value: -1.998 , 1.998
decision: do not reject Ho
p-value: 0.058
we do not have enough evidence to support the claim that difference in the average monthly cost per child for childcare outside the home between state supported facilities and privately owned facilities