Question

Please show work

9.) Are a person's college & the photo -upload ing site s/he chooses independent? Below is a list of randomly sampled college students who were asked which of the following photo-uploading site s/he most prefers. Our goal is to determine whether these two variables are dependent. Let = 0.1 Instagram G0ogle+ Facebook Observed Foothill 21 10 13 De Anza 21 12 12 5 SJSU 16 7 a) State the null & alternative hypotheses, in the context of the problem. b) Describe the type I & type II errors, in the context of the problem. c) Calculate the expected frequency table. d) Use your TI to calculate the test statistic & p-value. Sketch the region whose area the p-value represents (label the important value along the horizontal axis). Define the p-value in the context of the problem. e) Make your conclusion in the context of the problem. Explain why.

Answer 1

a) We will set up the null hypothesis that

Persons college and photo uploading sites are dependent

Ho 0

Persons college and photo uploading sites are independent

H1

b) Type I error is rejecting null hypothesis (H₀) When null hypothesis (H₀) was actually True and Type II error is accepting null hypothesis (H₀) When Alternate hypothesis (H₁) was actually True.

c) Under the null hypothesis the test statistics is

2=(-E Ei (Oi E2

Where Oi is the observed frequency where Ei is the expected frequency and is obtained as follow

  

RC Ei = N

Where R and C are row and column total frequencies and N is the Total frequency

The expected frequencies are given below

Observed	Facebook	Instagram	Google+	Total
Foothill	20.10	13.51	10.39	44
De Anza	20.55	13.82	10.63	45
SJSU	17.35	11.67	8.98	38
Total	58	39	30	127

(21-20.10) (10-13.51) + (5 8.98)2 20.10 13.51 8.98

=6.337

The degrees of freedom is (c-1)(r-1)=(3-1)(3-1)=4

and corresponding P.Value at 4 degrees of freedom = 0.175333

The Tabulated Chi square at 1% significance level with 4 degree of freedom = 13.277

The area under dark black represents P.Value area in the below graph

Distribution Plot Chi-Square, DF-4 0.20 0.15 0.10 0.05 0.00 14 0 2 4 8. 10 12 16 X Density 9

e) Since calculated P.Value = 0.175333 which is greater then 0.01, we will accept null hypothesis and concludes that Persons college and photo uploading sites are dependent.