Question

You have now been asked to study the yearly mean sales of cameras of two competing models at stores throughout the United States. You will also study the proportions of cameras sold that include certain lenses at a large store that sells both lenses. The specific questions you will be asked to answer are stated below. In addition, appropriate sample data for the studies you will be accomplishing are given below. Answer the following questions concerning the situations posed.

2) Once again, as has happened in the past, you are very much in doubt concerning the validity of the known population standard deviations, this time for each camera body, in the yearly sales of the two brands of camera bodies. Therefore, you wish to conduct your study with the knowledge that the population standard deviations are unknown. You collect random samples of the yearly sales of the two camera bodies at populations of stores. The data that has been collected is shown in appendix one below. At both the 10% and 5% levels of significance, are there any differences in the mean sales of the two camera bodies at the two populations of stores? Again, if the software makes it possible, find both 90% and 95% confidence intervals for the difference in the mean sales of the camera bodies between the two populations of stores. Explain the meanings of these intervals. Then, if possible, based upon the procedures you have chosen to address the problem, use the intervals to supplement and test whether there is a difference in the mean sales of the two camera bodies between the two populations of stores.

Nikon D5:

131     145     150     156     176     154     138     122     130     235     165     168     221     229     154     155     154     160     154      144     240     143     232     238     130

Canon Model:

      138     140     237     147     170     155     232     228     135     130     161     160     220     229     155     158     150     250     248      246     139     233     133     230     126    

Answer 1

we use R-software to find the confidence interval, r-codes are given below

> Nikon_D5=c(131,145,150,156,176,154,138,122,130,235,165,168,221,229,154,155,154,160,154,144,240,143,232,238,130)
> m1=mean(Nikon_D5)
> m1
[1] 168.96
> s1=sqrt(var(Nikon_D5))
> s1
[1] 38.58808
> Canon_Model=c(138,140,237,147,170,155,232,228,135,130,161,160,220,229,155,158,150,250,248,246,139,233,133,230,126)
> m2=mean(Canon_Model)
> m2
[1] 182
> s2=sqrt(var(Canon_Model))
> s2
[1] 45.92839
> t.test(Nikon_D5,Canon_Model,var.equal=T,conf.level=0.90)

   Two Sample t-test

data: Nikon_D5 and Canon_Model
t = -1.0869, df = 48, p-value = 0.2825
alternative hypothesis: true difference in means is not equal to 0
90 percent confidence interval:
-33.162376 7.082376
sample estimates:
mean of x mean of y
168.96 182.00

> t.test(Nikon_D5,Canon_Model,var.equal=T,conf.level=0.95)

   Two Sample t-test

data: Nikon_D5 and Canon_Model
t = -1.0869, df = 48, p-value = 0.2825
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-37.16244 11.08244
sample estimates:
mean of x mean of y
168.96 182.00
Conclusion: Here from the above output 90% confidence interval is ( -33.162376, 7.082376) and 95% confidence interval is  (-37.16244 11.08244), here value zero lies between both interval therefore we may conclude that the mean sales of the two camera bodies between the two populations of stores are same.

(# hope this will help you. if any difficulty feel free to comment. Thank you)