Question

Please answer both parts for upvote

part a) Consider the shape of the distribution of each of the following scenarios. For each, answer the following questions:

Scenario 1 - The heights of female adults in Halifax

Scenario 2 - The average number of children that Canadian families have.

For each, answer the following questions:

1. What shape would you expect the distribution to have, and why?

2. If we randomly select a sample of 25 from that population, would the central limit theorem hold? Explain.

part b)

Many university students travel to attend school. We randomly selected 50 Intro stats students at MSVU and asked if they are a Canadian Citizen. There were 44 who said yes they are.

Identify the W’s for the sample.

Who: What: Where: When: Why

Is this a survey, observational study or experiment? Explain.

Population:

Parameter:

Sample:

Sample statistic:

Answer 1

Scenario 1 - The heights of female adults in Halifax

The shape would we expect the distribution of heights of female is approximately symmetric around the mean height because the hight in general more concentrated around its mean value .

Since the distribution of heights of female adults in Halifax is approximately symmetric the sample size n = 25 is sufficient for used Central Limit Theorem (CLT)

Scenario 2 - The average number of children that Canadian families have.

The frequency of the children is more around 1 and 2 and then decline. But some families have 4 or 5 or 6 children also. So the distribution is positively skewed.

Since the shape is not symmetric, the sample size n = 25 is not sufficient for used of central limit theorem.

b) This is survey of students as Canadian Citizen or not

Population : All the Intro Stats students at MSVU

Parameter of Interest : Proportion of Canadian Citizen among them.

Sample : 50  Intro stats students at MSVU

Sample statistic = p = 44/50 = 0.88