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 using only PHStat in Excel along with business explanations.

In addition, you wish to concern yourself with a comparison of the proportions of the sales of the two camera bodies that include the purchase of a certain lens that fits the body of the camera being studied. Just as the camera bodies are considered competing models, so are the two lenses that may or not be included with the sales of the camera bodies. Random samples of yearly sales of both camera bodies are selected. It is observed with each purchase whether the lens has also been purchased. The data concerning whether the lens is included with the purchase of the camera body is shown in appendix two below. At each of the 10% and 5% levels of significance, is the proportion of Nikon D5 purchases that include the purchase of a certain type of lens at the same time less than the proportion of Canon purchases that includes the purchase of an equivalent Canon lens? If possible, construct both 90% and 95% confidence intervals for the difference in the population proportions of sales of the camera bodies at the stores that include the sale of the lenses. Explain their meaning. Do not use these intervals to perform any hypothesis tests. Make sure to use PHStat in Excel to solve the problem!

Appendix Two: (Includes the Purchase of a Lens? Y = yes, N = no)

Nikon D5:

      Y N N N Y Y N Y N Y Y N N N N Y Y Y N Y Y N N N N N N Y N N N Y N N N N

      

Canon Model:

      N N Y Y Y N N Y N Y N N Y Y Y Y N N N N Y N Y N Y N N N Y Y Y Y Y N Y Y

Answer 1

At each of the 10% and 5% levels of significance, is the proportion of Nikon D5 purchases that include the purchase of a certain type of lens at the same time less than the proportion of Canon purchases that includes the purchase of an equivalent Canon lens?

Hypothesis

Ho: p1​ = p2​

Ha: p1​ < p2​

Data:

Nikon D5:

Y

N

N

N

Y

Y

N

Y

N

Y

Y

N

N

N

N

Y

Y

Y

N

Y

Y

N

N

N

N

N

N

Y

N

N

N

Y

N

N

N

N

Canon Model:

N

N

Y

Y

Y

N

N

Y

N

Y

N

N

Y

Y

Y

Y

N

N

N

N

Y

N

Y

N

Y

N

N

N

Y

Y

Y

Y

Y

N

Y

Y

	Nikon D5:	Canon Model:
Total Sample (n1, n2)	36	36
Lense purchase alongwith	13	19
Proportion (p1,p2)	0.361111111	0.527777778

The value of the pooled proportion is computed as

=

Also, the given significance level is =

The z-statistic is computed as follows:

Using the P-value approach: The p-value is p = 0.0774p=0.0774, and since p = , the null hypothesis is not rejected and it is concluded that 5% levels of significance proportion of Nikon D5 purchases that include the purchase of a certain type of lens at the same time is not less than the proportion of Canon purchases that includes the purchase of an equivalent Canon lens.

2) Also, the given significance level is = 0.10

The z-statistic is computed as follows:

Using the P-value approach: The p-value is

Hence the null hypothesis is rejected and it is concluded that 10% levels of significance proportion of Nikon D5 purchases that include the purchase of a certain type of lens at the same time is less than the proportion of Canon purchases that includes the purchase of an equivalent Canon lens.

90% confidence interval : ()

95% confidence interval : (=0.05)