Question

You also have been asked to study whether there are any differences in the proportions of the yearly sales of various Nikon camera bodies concerning whether a purchase of the body includes the purchase of a lens that fits the camera at the time of the purchase of the body. Random samples of yearly sales at stores throughout the country of these various camera bodies are taken. The sample data concerning sales of the camera bodies with and without the purchase of a lens is shown below in appendix two. At each of the 10% and 5% levels of significance, are there any differences in the proportions of the sales of the camera bodies concerning whether a lens is also purchased? If, at either level of significance, you find any differences in the proportions of sales of the units concerning the purchase of a lens, perform the necessary work in order to ascertain where any possible differences lie.

Appendix Two:

                                                            Camera Body

Purchase a Lens?       D5              D850              D7500            D7200

            Yes                      82             76                 48                 39

            No                        66             68                 21                 11

Answer 1

The hypothesis being tested is:

H₀: There any no differences in the proportions of the sales of the camera bodies concerning whether a lens is also purchased

H_a: There any differences in the proportions of the sales of the camera bodies concerning whether a lens is also purchased

observed	expected	O - E	(O - E)² / E
82	61.250	20.750	7.030
76	61.250	14.750	3.552
48	61.250	-13.250	2.866
39	61.250	-22.250	8.083
245	245.000	0.000	21.531
21.53	chi-square
3	df
.0001	p-value

The p-value is 0.0001.

Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there any differences in the proportions of the sales of the camera bodies concerning whether a lens is also purchased.

At the 0.05 level:

	pi	pj	n1	n2	Difference	CV	Significantly different?
D5 vs D850	0.554054	0.527778	148	144	0.026276	0.163008	No
D5 vs D7500	0.554054	0.695652	148	69	-0.1416	0.192419	No
D5 vs D7200	0.554054	0.78	148	50	-0.22595	0.199666	Yes
D850 vs D7500	0.527778	0.695652	144	69	-0.16787	0.19366	No
D850 vs D7200	0.527778	0.78	144	50	-0.25222	0.200862	Yes
D7500 vs D7200	0.695652	0.78	69	50	-0.08435	0.225386	No

At the 0.10 level:

	pi	pj	n1	n2	Difference	CV	Significantly different?
D5 vs D850	0.554054	0.527778	148	144	0.026276	0.145794	No
D5 vs D7500	0.554054	0.695652	148	69	-0.1416	0.172099	No
D5 vs D7200	0.554054	0.78	148	50	-0.22595	0.178581	Yes
D850 vs D7500	0.527778	0.695652	144	69	-0.16787	0.173209	No
D850 vs D7200	0.527778	0.78	144	50	-0.25222	0.179651	Yes
D7500 vs D7200	0.695652	0.78	69	50	-0.08435	0.201585	No