Question

2 Use Excel to find the following confidence intervals 110points total The feollowing data show the namber of paid vacation days for a random sample of 20 employees from PSU A1 a) Find the 95% confidence interval fr the average number of vacation days. (2 points for output. I point fr ower limit, I point for upper limit Copy the data below your name in cell A3 in Excel. Select the tab labeled Duta, then select Data Analysis If your data analysis button is not installed, go back to the diroctions for installation before you continue with the est of this lab In the Data Analysis Tool, select Descriptive Statistics, then 0 12 Data Analysis 13 15 16 17 19 21 Click into the box next to Input Range. Use your mouse and highlight the data including the label. Check the bat dat says-Labels in fiN ย-"If you dd not select be label for you nput range then dn't check the label box. Click the circle next to Output Range. Click into the hox to the right of output rangs Use your mouse and loct a cell whare you wani the top left corser of your table so show. Check the thoxes nE to Summary Statistics and Confidence Level for Mcan Change your confidance level to fit the question Seloct OK 25 26 27 Descriptive Statstics 31 32 35 36 37 The table that is peoduced does not give you the confidence interval, however it dees give you the sample mean and the margin of arror. The margin of error is the last row called Confdence Level. To find the confidlence intcrval suberact and add the margin of errex to the mean in two sparate oells to the right of the uble Round your answers to two decimal places. Highligh hese two nubors in bluc. I will be selecting each cell so check Click into the box next to Input Range. Use your mouse and highlight the data including the label. Check the box that says "Labels in first row." If you did not select the label for you input range then don't check the label box. Click the circle next to Output Range. Click into the box to the right of output range. Use your mouse and select a cell where you want the top left corner of your table to show. Check the boxes next to Summary Statistics and Confidence Level for Mean.Change your confidence level to fit the question. Select OK Descriptive Statistics Input AS3-5A523 nput Range Cancel columns Grouped By O Bows Help Labels in first row Output options ⓔ Ω.tput Range O Nrw worksheet SCS3 y: ONew workbook 2 Summary statistics Coghdence Level for Mear kth Largest 95 The table that is produced does not give you the confidence interval, however it does give you the sample mean and the margin of error. The margin of error is the last row called Confidence Level. To find the cor interval subtract and add the margin of error to the mean in two separate cells to the right of the tabic. Round your answers to two decimal places. Highlight these two numbers in blue. I will be selecting each cell to check on the formulas so do not just type in the answer from a calculator b) Put your answer in interval notation just below the two cells that you subtracted and added. For example if the mean was 20 and the margin of error was 2.45, your interval would be (17.55, 22.45). (1 point) c) Type in an interpretation of your interval using context and units from the question. Check the typed lecture for examples. (1.5 points) d) Find the 99% confidence interval for the average number of vacation days. Repeat what you did in part a, but change the confidence level for mean to 99%. Round your answers to two decimal places. Highlight the two cells with the lower and upper boundaries. I will be selecting each cell to check on the formulas so do not just type in the answer from a calculator. (I point) e) Put your confidence in interval notation.(1 point) ) Which confidence interval is smaller (narrower) on the number line? (0.5 point) Which interval is more likely to contain the population mean, explain your answer? (I point) g)

Answer 1

(1-alpha)*100% confidence interval for population mean=sample mean±t(alpha/2,n-1)*s/sqrt(n)

(a) 95% confidence interval for population mean=22.75±2.093*14.003/sqrt(20)=22.75±6.554=(16.196,29.304)

(b)(16.196,29.304)

(c) if the hypothetical value lies in this interval, we accept null hypothesis other wise reject

(d)99% confidence interval for population mean=22.75±2.861*14.003/sqrt(20)=22.75±8.958=(13.792,31.708)

(e)(13.792,31.708)

(f) 95% confidence interval is narrower as its margin of error is less

(g) 99% confidence interval would have more chance as it has higher confidence level and accordingly wider interval and  higher margin of error

	t-value	margin of error	lower limit	upper limit
95% confidence interval	2.093	6.554	16.196	29.304
99% confidence interval	2.861	8.958	13.792	31.708

following data have been used to find the confidence interval

x
3
21		n=	20
2		mean=	22.75
28		sample sd=s=	14.00329
5
25
4
21
19
33
15
27
17
27
27
29
21
43
27
61