# Value of Consumption

(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.

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