Question

For each problem in this assignment, first use hypothesis testing to answer the question. Then create a confidence interval/bound as needed regarding the problem and provide an estimate of the p-value associated with the result. The estimate of the p-value may be a bound and not an exact value.

1. My children went to college in towns that are south of Rochester, but at about the same latitude. I wondered if they both experienced about the same temperatures. To answer this question, I went to wunderground.com, and I recorded the average high temperature on the 6^th day of each month for each location. The data and any possible summary statistics you might need to work this problem are provided below. Can you tell me if there was a difference in average temperature for my 2 children? Use a = 0.10 and remember to include all 5 steps and an estimation or bounds on the p-value.

month	Philly	Indy	Philly - Indy
Jan	40	38	2
Feb	38	40	-2
Mar	49	50	-1
Apr	60	62	-2
May	71	71	0
Jun	80	81	-1
Jul	87	84	3
Aug	86	84	2
Sep	81	82	-1
Oct	70	70	0
Nov	60	59	1
Dec	48	43	5
average	64.2	63.7	0.5
standard deviation	17.6	17.6	2.15

Answer 1

month	Philly	Indy
Jan	40	38
Feb	38	40
Mar	49	50
Apr	60	62
May	71	71
Jun	80	81
Jul	87	84
Aug	86	84
Sep	81	82
Oct	70	70
Nov	60	59
Dec	48	43
t-Test: Two-Sample Assuming Equal Variances
	Philly	Indy
Mean	64.16666667	63.6666667
Variance	309.7878788	310.424242
Observations	12	12
Pooled Variance	310.1060606
Hypothesized Mean Difference	0
df	22
t Stat	0.069548938
P(T<=t) one-tail	0.472590494
t Critical one-tail	1.321236742
P(T<=t) two-tail	0.945180987
t Critical two-tail	1.717144374

After Entering the values in Excel we can easily analyse the difference of means between phily and Indy variable

steps to do in Excel

1) Enter Values in Excel as shown above in Image

2 ) Go to Data tab and click Data analysis - t-Test: Two-Sample Assuming Equal Variances - Select two variables range and put alfa = 0.10

and click OK to get the results.

Here

we can see from the above results that p values is 0.95 > = 0.10 which Implies Ho is We do not reject Ho

Which implies that Average temperature of Philly and Indy are not different at = 0.10 level of Significance