(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.