Question

40 individuals were surveyed and asked the following question: How many days a week do you typically exercise? The table below shows the responses. Use the following table to answer the questions below.

Names	How many times a week do you typically exercise?
1	6
2	5
3	6
4	4.5
5	5
6	6
7	5
8	3
9	6
10	4
11	5
12	6
13	4
14	6
15	6
16	3
17	3
18	5
19	5
20	6
21	3
22	3
23	5
24	6
25	6
26	5
27	5
28	5
29	5
30	5
31	8
32	5
33	5
34	6
35	4
36	5
37	3
38	3
39	4
40	4

1. Calculate the average and standard deviation of the responses.

Average = ________

Standard Deviation = ________

2. Calculate the appropriate SE based on the number of individuals who responded and #1 above. SHOW THE CALCULATION.

3. Calculate a 90% confidence interval for the average value of the table above. SHOW ALL CALCULATIONS.

4. Interpret the full meaning of the confidence interval you have in #3. Remember to include all four components to an interpretation.

Answer 1

Solution-1:

dev=wee_exe -xbar

devsq=dev*dev

wee_exe xbar dev devsq
1 6.0 4.8625 1.1375 1.29390625
2 5.0 4.8625 0.1375 0.01890625
3 6.0 4.8625 1.1375 1.29390625
4 4.5 4.8625 -0.3625 0.13140625
5 5.0 4.8625 0.1375 0.01890625
6 6.0 4.8625 1.1375 1.29390625
7 5.0 4.8625 0.1375 0.01890625
8 3.0 4.8625 -1.8625 3.46890625
9 6.0 4.8625 1.1375 1.29390625
10 4.0 4.8625 -0.8625 0.74390625
11 5.0 4.8625 0.1375 0.01890625
12 6.0 4.8625 1.1375 1.29390625
13 4.0 4.8625 -0.8625 0.74390625
14 6.0 4.8625 1.1375 1.29390625
15 6.0 4.8625 1.1375 1.29390625
16 3.0 4.8625 -1.8625 3.46890625
17 3.0 4.8625 -1.8625 3.46890625
18 5.0 4.8625 0.1375 0.01890625
19 5.0 4.8625 0.1375 0.01890625
20 6.0 4.8625 1.1375 1.29390625
21 3.0 4.8625 -1.8625 3.46890625
22 3.0 4.8625 -1.8625 3.46890625
23 5.0 4.8625 0.1375 0.01890625
24 6.0 4.8625 1.1375 1.29390625
25 6.0 4.8625 1.1375 1.29390625
26 5.0 4.8625 0.1375 0.01890625
27 5.0 4.8625 0.1375 0.01890625
28 5.0 4.8625 0.1375 0.01890625
29 5.0 4.8625 0.1375 0.01890625
30 5.0 4.8625 0.1375 0.01890625
31 8.0 4.8625 3.1375 9.84390625
32 5.0 4.8625 0.1375 0.01890625
33 5.0 4.8625 0.1375 0.01890625
34 6.0 4.8625 1.1375 1.29390625
35 4.0 4.8625 -0.8625 0.74390625
36 5.0 4.8625 0.1375 0.01890625
37 3.0 4.8625 -1.8625 3.46890625
38 3.0 4.8625 -1.8625 3.46890625
39 4.0 4.8625 -0.8625 0.74390625
40 4.0 4.8625 -0.8625 0.74390625

average=sum(wee_exe )/total wee_exe

= 194.5/40

=4.8625

standard deviation=sqrt(sum(devsq/n-1)

=sqrt(52.49375/40-1)

= 1.16017

AVERAGE=xbar=4.8625

STANDARD DEVIATION=s=1.16017

Solution-2:

standard error=s/sqrt(n)=1.16017/sqrt(40)=0.183439

Solution-3:

alpha=0.10

alpha/2=0.10/2=0.05

df=n-1=40-1=39

t critical in excel is

=T.INV(0.05,39)

=1.684875122

90% confidence interval for mean is

xbar-t*s/sqrt(n),xbar+t*s/sqrt(n)

4.8625-1.684875122*0.183439,4.8625+1.684875122*0.183439,

4.553428,5.171572

90% lower limit mean=4.553428

90% upper limit mean=5.171572

4. Interpret the full meaning of the confidence interval you have in #3. Remember to include all four components to an interpretation.

we are 90% confident that the true mean days a week one   typically exercise lies in between

4.553428 and 5.171572