Please solve these questions using stat tools in excel and interpret the results
ID: 3356560 • Letter: P
Question
Please solve these questions using stat tools in excel and interpret the results.
Link for excel - "Budgetmart" https://drive.google.com/file/d/0BwnfLKPdeFBbZEhuUXRhTzZyUlE/view?usp=sharing
3) Let uF and uM be the average salaries of female and male customers, respectively. a) Find a 90% confidence interval for uF. Do the same for uM. Can you use this result to conclude with 90% confidence that the average salary of male customers is higher than that of female customers? Why and why not? Explain. b) Find a 90% confidence interval for uF – uM and interpret the result. Is your finding consistent with that of part (a)?
4. Let µ1 be the average amount spent by customers whose education level is high school or below and µ2 be the average amount spent by customers who has college or graduate degree. Construct a 95% confidence interval for µ1 - µ2. Interpret the result. Do customers with higher education levels spend on average significantly more than those with lower education levels? Explain.
Explanation / Answer
a) Find a 90% confidence interval for uF. Do the same for uM. Can you use this result to conclude with 90% confidence that the average salary of male customers is higher than that of female customers? Why and why not? Explain
We have given the data set.
Now we have to find 90% confidence interval for population means for female and male.
Here we use one sample z-interval since sample size is > 30.
90% confidence interval for population mean is,
Xbar - E < mu < Xbar + E
where Xbar is sample mean.
E is margin of error.
E have formula,
E = (Zc * sigma) / sqrt(n)
Zc is critical value for normal distribution.
Zc we can find using EXCEL.
syntax :
=NORMSINV(probability)
where probability = 1 - a/2
where a = 1 - C
For 90% confidence Zc = 1.645
Now sample statistics for male and female are,
Variable gender1 N Mean SE mean
salary1 0 10 103829 6272
1 21 95590 4897
Confidence interval for female :
E = 1.645*6272 = 10317.44
Lower limit = Xbar - E = 103829- 10317.44 = 93511.56
Upper limit = Xbar + E = 103829 + 10317.44 = 114146.4
90% confidence interval for female is (93511.56, 114146.4)
We are 90% confident that the population mean for female is in between 93511.56 and 114146.4.
Confidence interval for male :
E =1.645*4897 = 8055.565
Lower limit = Xbar - E = 95590 - 8055.565 = 87534.44
Upper limit = Xbar + E = 95590 + 8055.565 = 103645.6
90% confidence interval for population mean for male is (87534.44, 103645.6)
We are 90% confident that the population mean for male is lies between 87534.44 and 103645.6.
b) Find a 90% confidence interval for MuF – MuM and interpret the result. Is your finding consistent with that of part (a)?
Now we have to find 90% confidence interval for muF-muM.
90% confidence interval for muF-muM is,
(X1bar - X2bar) - E < mu1 - mu2 < (X1bar - X2bar) + E
where X1bar is sample mean for female
X2bar is sample mean for male.
E is margin of error.
E = Zc * sqrt(s12 / n1 + s22 / n2)
90% confidence interval for mu1-mu2 is (-5904, 22382).
We are 90% confident that the difference in population mean is lies between -5904 and 22382.