Question

In: Statistics and Probability

A social worker was interested in determining whether there is a significance difference in the average...

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))

Solutions

Expert Solution

Given that,
mean(x)=705
standard deviation , sigma1 =95
number(n1)=64
y(mean)=675
standard deviation, sigma2 =80
number(n2)=64
null, Ho: u1 = u2
alternate, H1: μ1 != u2
level of significance, alpha = 0.05
from standard normal table, two tailed z alpha/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) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=705-675/sqrt((9025/64)+(6400/64))
zo =1.932
| zo | =1.932
critical value
the value of |z alpha| at los 0.05% is 1.96
we got |zo | =1.932 & | z alpha | =1.96
make decision
hence value of | zo | < | z alpha | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.932 ) = 0.05331
hence value of p0.05 < 0.05331,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: μ1 != u2
test statistic: 1.932
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.05331
we do not have enough evidence to support the claim that 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
Answer:
option:D
test statistic: 1.932


Related Solutions

A businesswomen was interested in determining whether there is a significant difference in the average monthly...
A businesswomen was interested in determining whether there is a significant 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 were selected yielding the following information: State Supported Facilities Privately Owned facilities Sample Size 64 64 Sample Mean 725 675 Standard Deviation 95 80 Find a 90% confidence interval for the true difference in average monthly cost of the childcare.    Based on the...
the leaders of the study are interested in the determining whether there is a difference in...
the leaders of the study are interested in the determining whether there is a difference in mean annual contributions for individuals covered by TSA's and those with 401(k) retirements program. you can use the results form the following table to test if the population mean of individual covered by TSAs is higher than those covered by 401(k). TSA    401(K) n1 = 8    n2=10 x1= 322.5 x2=298.3 s1=48.3 s2= 53.3 1. Formulate the appropriate null and alternative hypotheses 2....
A social scientist is interested in determining if there is a significant difference in the proportion...
A social scientist is interested in determining if there is a significant difference in the proportion of people who report working full time between two groups: those with a high school education or less (Group 1) and those with an associates’s degree or higher (Group 2). Using data from the General Social Survey, the researcher obtains the following table: Education Working Full Time Other Employment Status Total No College (Group 1) 500 764 1264 At Least Some College (Group 2)...
A social scientist is interested in determining if there is a significant difference in the proportion...
A social scientist is interested in determining if there is a significant difference in the proportion of people who report working full time between two groups: those with a high school education or less (Group 1) and those with an associates’s degree or higher (Group 2). Using data from the General Social Survey, the researcher obtains the following table: Education Working Full Time Other Employment Status Total No College (Group 1) 500 764 1264 At Least Some College (Group 2)...
A stock market investor is interested in determining whether there is a significant difference in the...
A stock market investor is interested in determining whether there is a significant difference in the P/E (price to earnings) ratio for companies from one year to the next. Six companies are randomly selected and their P/E ratios for Year 1 and Year 2 are recorded. Are the P/E ratios for Year 1 greater than for Year 2? Use a 10% level of significance. Company c Year 1 16 29 36 23 12 19 Year 2 13 25 31 20...
A stock market investor is interested in determining whether there is a significant difference in the...
A stock market investor is interested in determining whether there is a significant difference in the P/E (price to earnings) ratio for companies from one year to the next. Six companies are randomly selected and their P/E ratios for Year 1 and Year 2 are recorded. Are the P/E ratios for Year 1 greater than for Year 2? Use a 10% level of significance. Company c Year 1 16 29 36 23 12 19 Year 2 13 25 31 20...
The manager at the Lawrence National Bank is interested in determining whether there is a difference...
The manager at the Lawrence National Bank is interested in determining whether there is a difference in the mean time that customers spend completing their transactions depending on which of four tellers the use. To conduct the test, the manager has selected simple random samples of 15 customers for each of the tellers and has timed them (in seconds) from the moment they start their transaction to the time the transaction is completed and they leave the teller station. The...
The manager at the Lawrence National Bank is interested in determining whether there is a difference...
The manager at the Lawrence National Bank is interested in determining whether there is a difference in the mean time that customers send completing their transactions depending on which of the four tellers they use. To conduct the test, the manager has selected simple random samples of 15 customers for each of the tells and has time them (in seconds) from the moment they start the transaction to the time the transaction is complete and they leave the teller station....
Researchers were interested in determining whether there was a difference in crime rates in areas where...
Researchers were interested in determining whether there was a difference in crime rates in areas where there is high youth unemployment vs low youth unemployment. Alpha (level of significance) was set at .05. State the null and alternate hypotheses. What is the independent variable? What is the dependent variable? Complete the table below: Low Youth Unemployment High Youth Unemployment Sample Size Sample Mean Sample Standard Deviation Estimated Standard Error Group Statistics High Youth Unemployment N Mean Std. Deviation Crime rate...
.You are interested in determining whether there is a statistically significant difference between economics and political...
.You are interested in determining whether there is a statistically significant difference between economics and political science majors in terms of their overall grade point average (GPA). You randomly sample 10 economics majors and 16 political science majors. You find that the average economist has a 3.0 GPA with a standard deviation of 0.4, and the average political scientist has a 3.4 GPA with a standard deviation of 0.3. Conduct a two-tailed hypothesis test using significance level α = 0.05....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT