15 MCQs in Statistics

  

(1) Which statement best describes what 90% confidence means, in the context of a 90% confidence interval to estimate a proportion? 

If we repeat this procedure lots of times, 90% of the time the sample value will be in this interval. 

If we repeat this procedure lots of times, then 90% of reasonable people would calculate this interval. If we repeat this procedure lots of times, 90% of the time we will get the right interval. 

If we repeat this procedure lots of times, 90% of the time the interval will contain the true value. 

If we repeat this procedure lots of times, 90% of intervals will be like the one we calculate. 

(2) We are going to estimate the proportion of companies that made a profit last year by taking a random sample and then constructing a 95% confidence interval. Anecdotal evidence suggests that only 30% of companies made a profit. What sized sample would be needed if we require the margin of error to be 0.02? 2016 2401 2017 4549 

Calculate the LOWER LIMIT of the 90% CI estimate for the proportion of students who buy their lunch most days if a random sample of 100 of them showed that 51 bought their lunch most days. (You don't need to check the conditions: assume they hold) Use three decimal places for your Z value and avoid rounding off too early. Write your answer to 2 decimal places. 

(3) A 95% confidence interval for the proportion of voters who approve of a new Government policy has been constructed as (0.66, 0.70). Which of the following is the best interpretation of this interval? 

Between 66 and 70% of voters approve of this policy. 

We are 95% confident that between 66 and 70% of voters in our sample approve of this policy. 

Between 66 and 70% of voters in our sample approve of this policy. 

We are 95% confident that between 66 and 70% of voters approve of this policy. 

95% of voters approve of this policy.

(4) In a regression analysis where quantity is regressed on price, the estimated equation is given by: Estimated quantity = 100 - 2 Price. Suppose that one of the data points was price = 20 and quantity = 50. What is the residual for this point? 

30 

-10 

10 

40 

-30 

(5) A student has used regression to forecast that consumption will be $90m when income is $100m and then interprets this as "Consumption will be 90m." What's wrong with that statement? Choose as many as are applicable. 

The analyst has made a mistake because this is an unlikely value. 

Consumption must be less than half of income. 

We can only estimate on average. 

Units ($) have been omitted. 

This is an estimate only and may not be correct. 

The interpretation should include that this is most probably the exact value of consumption. 

(6) According to the 68-95-99.7 rule, within what bounds will we expect 95% of values lie if we have a mound shaped distribution with a mean of 40 and a variance of 9? 

34, 46 

37, 43 

22, 58 

31, 49 

13, 67 

(7) In a standard Normal model, what value of Z cuts off the highest 3% of values? 

0.84 

1.88 

0.618 

0.242 

0.382 

(8) Find the standard deviation of a Normal model with mean 0.50 if 20% of values are BELOW 

0.38. 

0.84 

0.2 

0.1 

0.14 

1.43

(9) What is meant by the sampling distribution of the sample proportion? 

The distribution of possible samples that we could take, each of the same size. 

The distribution of the sample values from taking one very large sample. 

The sample proportion that would be likely to occur from a random sample providing the sample is large. 

The sample proportion that would be likely to occur from a random sample of any size. 

The distribution of possible values of the sample proportion, when we take repeated samples each of the same size, and calculate the proportion from each one. 

(10) A random sample of size 100 is drawn from a population with mean 48 and variance 25. What is the variance of the sample mean? 

2 

0.25 

20 

4 

0.4 

(11) We know that 20% of students will fail a given assessment. We take a random sample of 36 students. Calculate the standard deviation of the sample proportion , the proportion who fail. 

0.4 

0.01

0.16 

0.067 

0.0044 

(12) Which of the following is the Central Limit Theorem? 

For a symmetric distribution, the measure of central tendency can be either the mean, median, or mode. 

The sample mean taken from a Normal population is Normal. 

Items in a random sample are independent. 

For large samples, the sample mean is approximately Normal, regardless of the shape of the parent population. 

The mean of the sample means is the population mean. 

(13) When we check the conditions for the sample proportion to be normal, one of the things we check is the success/failure condition. What does this say? 

The number of success and the number of failures must each exceed 10. 

The number of success and the number of failures must add to 10. 

The number of success OR the number of failures must exceed 10. 

The number of success and the number of failures don't matter providing we have a sample of at least 30. 

The number of success (np) must be below 10.

(14) Is the following statement true or is it false? "A CI is wider if we take a larger sample OR if we take a larger % confidence"

True.

False.

(15) Which of the following would indicate a regression is a poor fit?

A high standard deviation of Y.

A positive slope.

A correlation close to -1.

A high value of R2.

A high standard error of estimate