Question

Hypothesis Testing and Confidence Intervals

The Reliable Housewares store manager wants to learn more about the purchasing behavior of its

"credit" customers. In fact, he is speculating about four specific cases shown below (a) through (d) and

wants you to help him test their accuracy.

b. The true population proportion of credit customers who live in an urban area exceeds 55%

i. Using the dataset provided in Files perform the hypothesis test for each of the above speculations (a) through (d) in order to see if there is an statistical evidence to support the manager’s belief. In each case,

oUse the

Seven Elements of a Test of Hypothesis, in Section 7.1 of your textbook (on or about Page 361) or the Six Steps of Hypothesis Testing I have identified in the addendum.

oUse α=2%for all your analyses,

oExplain your conclusion in simple terms,

oIndicate which hypothesis is the“claim”,

o Compute the p-value,

o Interpret your results,

ii.Follow your work in (i) with computing a 98% confidence interval for each of the variables

described in (a) though (d). Interpret these intervals.

iii.

Write an executive summary for the Reliable Housewares store manager about your analysis,

distilling down the results in a way that would be understandable to someone who does not

know statistics. Clear explanations and interpretations are critical.

Location	Income ($1000)	Size	Years	Credit Balance ($)
Rural	30	2	12	3,159
Rural	31	2	4	1,864
Rural	37	1	20	2,731
Rural	27	1	19	2,477
Rural	33	2	12	2,514
Rural	44	1	7	2,995
Rural	42	2	19	3,020
Rural	30	1	14	2,583
Rural	50	2	11	3,605
Rural	35	1	11	3,121
Rural	27	2	1	2,921
Rural	30	2	14	3,067
Rural	22	4	16	3,074
Rural	53	1	7	2845
Suburban	32	4	17	5,100
Suburban	50	5	14	4,742
Suburban	66	4	10	4,764
Suburban	63	4	13	4,965
Suburban	62	6	13	5,678
Suburban	55	7	15	5,301
Suburban	54	6	14	5,573
Suburban	67	4	13	5,037
Suburban	22	3	18	3,899
Suburban	39	2	18	2,972
Suburban	54	3	9	3,730
Suburban	23	6	18	4,127
Suburban	61	2	14	4,273
Suburban	46	5	13	4,820
Suburban	66	4	20	5,149
Suburban	74	7	12	5394
Suburban	66	7	14	5036
Urban	54	3	12	4,016
Urban	55	2	9	4,070
Urban	40	2	7	3,348
Urban	51	3	16	4,110
Urban	25	3	11	4,208
Urban	48	4	16	4,219
Urban	65	3	12	4,214
Urban	55	6	15	4,412
Urban	21	2	18	2,448
Urban	37	5	5	4,171
Urban	21	3	16	3,623
Urban	41	7	18	4,828
Urban	48	2	8	3,866
Urban	34	5	5	3,586
Urban	67	5	1	5,345
Urban	55	6	10	5,370
Urban	52	2	11	3,890
Urban	62	3	2	4,705
Urban	64	2	6	4,157
Urban	29	4	4	3,890
Urban	39	4	15	4,183
Urban	26	7	17	4,603
Urban	44	6	5	3962
Urban	25	3	15	3442

Answer 1

Here , the true population proportion = 0.55...
A new sample data is there...
Where , the sample population proportion = (Total no. of credit customers who lives in urban area ) / Total no. of customers

= 24/ 55 = 0.436363636...

Now, to test :
H0 : The proportion of customers who lives in urban area = 0.55 vs

H1: The proportion of customers who lives in urban area > 0.55...

So, test statistic = (0.436363636 - 0.55) / SQRT ( 0.436363636 * (1- 0.436363636) / 55 )..........

= -1.699318926.....

P-VALUE = prob( test statistic > -1.699318926) =  0.044629554......

now, α=2%...so, p-Value > 0.02...

So, we can't reject the null hypothesis in favor of the alternative hypothesis
So, here, we can't say that the proportion of customers who lives in urban area exceeds 55%..

So. the result is, the proportion of credit customers who lives in urban area does not exceed 55%..while using our willingness to make a Type I error α = 0.02..

confidence interval =  0.436363636 ± ( z* SQRT ( 0.436363636 * (1- 0.436363636) / 55 )) , where z = p-value when α=2%...
so,z = -2.053748911...
so, confidence interval = ( 0.299025933 , 0.573701339).........

so, there is a 98% chance that the true proportion of credit customers who lives in urban area is in between (0.299025933 , 0.573701339).........