A sociologist was interested in determining if there

Gavin Weiss

Gavin Weiss

Answered question

2022-03-15

A sociologist was interested in determining if there was a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Use a Chi-Square independence test to determine if age and type of movie preferred are independent at the 5% level of significance.
 18-23 years old  24-29 years old  30-35 years old  Total  Drama 8151134 Science Fiction 1210830 Comedy 981229 Total 29333193
Provided the assumptions of the test are satisfied, find the test statistic χ2
a) 1.444
b) 12.234
c) 3.623
d) 2.944
e) Cannot be determined.

Answer & Explanation

Alexa Lewis

Alexa Lewis

Beginner2022-03-16Added 5 answers

It is given that the observed frequencies for the age of a young adult and the type of movies preferred.
Formula for chi-square test statistic:
χ2=t=1n(OiEi)2Ei
Observed Frequencies:
 18-23 years old  24-29 years old  30-35 years old  Total  Drama 8151134 Science Fiction 1210830 Comedy 981229 Total 29333193
Calculate the Expected Frequencies:
 Row Variable  18-23 years old  24-29 years old  30-35 years old  Total  Drama 34×2993=10.602234×3393=12.064534×3493=11.333334 Science Fiction 30×2993=9.354830×3393=10.645230×3193=1030 Comedy 29×2993=9.043029×3393=10.290329×3193=9.666729 Total 29333193
Calculate the chi-square test statistic value is as follows:
χ2=(810.6022)210.6022+(1512.0645)212.0645+(1111.3333)211.3333+(129.3548)2129.3548+(1010.6452)210.6452+
+(810)210+(99.0430)29.0430+(810.2903)210.2903+(129.6667)29.6667
=0.6387+0.7143+0.0098+0.7480+0.0402+0.4+0.0002+0.5097+0.5632
=3.6240
Therefore, the chi-square test statistic is 3.624.
From the given options, the chi-square test statistic is nearly equal to 3.623.
Therefore, the correct option is c) 3.623.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?