Question

1) Which of the following statements are true?

1. If the null hypothesis is rejected at the 1% level of significance, then it will be rejected at 5% of level of significance.

2. For a given confidence level, halving the margin of error requires a sample twice as large.

3. For a specified confidence level, larger samples provide smaller margins of error.

a) Ionly b) IIonly c) IIIonly d) IandIIonly e) IandIIIonly

2) Suppose that you take random samples of size n from a large population and compute ?, sample proportions of individuals who are left handed. Which of the following statements is TRUE?
a) The larger the sample size, the larger the width of a 95% confidence interval for the population proportion.
b) The larger the sample size, the smaller the bias. c) The larger the sample size, the smaller the margin of error. d) All of the above are true. e) None of the above are true.

3) Which of the following is not an example of a categorical variable?

a) the political party affiliation of a particular voter. b) the county of residence of a particular vote. c) the gender of a particular voter. d) the age of a particular voter. e) All of the above are categorical.

Answer 1

1) Which of the following statements are true?

a)If the null hypothesis is rejected at the 1% level of significance, then it will be rejected at 5% of level of significance

Here the strictness reduces if the level of significance increases. So at 1% which stricter is rejecting null then 5% will have the same result.True

b)For a given confidence level, halving the margin of error requires a sample twice as large.

Margin of Error as the square root of 'n' in the denominator. Since it is square root simply increasing twice does not half the MOE.False

c)For a specified confidence level, larger samples provide smaller margins of error.

Larger samples have more accuracy thus will reduce error. So MOE will reduce. True

e) I and IIIonly

2) Suppose that you take random samples of size n from a large population and compute ?, sample proportions of individuals who are left handed. Which of the following statements is TRUE?
a) The larger the sample size, the larger the width of a 95% confidence interval for the population proportion.

False

Larger sample have smaller MOE. So the interval is narrower. Thus width will be smaller.

b) The larger the sample size, the smaller the bias.

True

Bias is when there is chance of not all the samples having equal chance of being chosen or non-response. So there is more bias. When sample is large there is more chances of getting responses and more independence.

c) The larger the sample size, the smaller the margin of error.

True

d) All of the above are true.

e) None of the above are true.

3) Which of the following is not an example of a categorical variable?

categorical variable has no association with numerical values. like gender, movie genre ,etc.

a) the political party affiliation of a particular voter.

b) the county of residence of a particular vote.

c) the gender of a particular voter.

d) the age of a particular voter.

Age is numerical.

e) All of the above are categorical.