Question

In: Statistics and Probability

A motivational speaker is interested in the demographics of their shows’ attendees. A random sample of...

A motivational speaker is interested in the demographics of their shows’ attendees. A random sample of 1051 adults who attended their last show was taken and the gender and US Census region in which they lived were recorded and summarized in the table below:

Gender	Northeast	Midwest	South	West	Total
Male	118	120	219	115	572
Female	93	119	150	117	479
Total	211	239	369	232	1051

(a) Suppose the speaker is going to ignore gender and is interested in whether people attending the events are equally likely to be from the four regions of the USA. What is the appropriate hypothesis test the researcher could use?

i. Chi Squared Test for Independence

ii. Chi Squared Test for goodness of fit (where we know the contents of the box)

iii. Two Sample Z test for difference in proportions

iv. One Sample Z test for proportions

(b) Calculate the test statistic, degrees of freedom (if relevant), and p value for the test of whether people attending the events are equally likely to be from the four regions of the USA.

(c) Suppose the speaker is also interested in whether Gender and US Census region are independent. What would be the appropriate expected count under the null of independence for the cell: Females and South?

Expert Solution

Solution:

(a) Suppose the speaker is going to ignore gender and is interested in whether people attending the events are equally likely to be from the four regions of the USA. What is the appropriate hypothesis test the researcher could use?

Answer: ii. Chi-Squared Test for the goodness of fit (where we know the contents of the box)

(b) Calculate the test statistic, degrees of freedom (if relevant), and p-value for the test of whether people attending the events are equally likely to be from the four regions of the USA.

Answer:

(c) Suppose the speaker is also interested in whether the Gender and US Census region are independent. What would be the appropriate expected count under the null of independence for the cell: Females and South?

Answer:

The expected count for Females and South is:

orchestra answered 2 years ago

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