1.A company has estimated the standard deviation of individual sales transactions to be $2000. Approximately 100 sales transactions take place each week. What is an estimate of the standard error of the average weekly sales?
$5
$20
$100
$200
2. A commodity trader who usually makes around 25 transactions per week obtained the following graph showing the average transaction size in $1000 for each of the last 20 weeks. Each dot represents the weekly average (in $1000) of about 25 transactions.
By examining the graph, would you estimate the standard error for the weekly average of transaction sizes to be closest to $2,000, $20,000, or $50,000?
$20,000
$2,000
$50,000
3. A media rating company that publishes television ratings uses a random sample of 1600 households and finds that 20% watched a particular show in a given week. What is the approximate margin of error?
0.5%
1.0%
1.5%
2.0%
4. Polls showed that the two main candidates in the 2004 presidential election were nearly tied on the day before the election. To predict the winner, a newspaper would like to have a poll which has margin of error of 5%. Roughly how large a sample would be needed for such a poll? (Hint: since candidates are nearly tied, each has roughly 50% of the vote.)
400
625
1000
5. Using a random sample of 100 workers, researchers calculate a 95% confidence interval for the average hourly wage earned by construction workers in the city of Boston. This interval they calculate is from $18 to $26.
Does this mean we can say that roughly 95% of construction workers in the city earn hourly wages between $18 and $26?
We cannot answer with Yes or No here
Yes, 95% of the wages fall between $18 to $26
No, we are 95% confident that the average wage falls between $18 to $26
6.A hotel has 180 rooms. Past experience shows that only 84% of people who reserve rooms actually show up. If the hotel takes 200 reservations, what is the chance there will be enough rooms for the people who actually show up?
(Hint: You want to find the chance that, in the sample of 200 reservations, the percentage of those who show up will be 90% (180/200) or less, knowing that true population percentage is 84%.)
Approximately 95% chance
Approximately 99% chance
Approximately 99.5% chance
7. A health insurer wants to know if having a nurse available to answer simple questions over a telephone hotline could cut costs by eliminating unnecessary doctor visits. Records show the yearly cost of doctor visits has an SD of $300. They randomly select 225 families, give them access to the hotline, and record the costs of their doctor visits. In this sample, they find the average yearly cost per family to be $820. Find a 95% confidence interval for the yearly population average cost of doctor visits per family.
Approximately from $820 to $860
Approximately from $800 to $880
Approximately from $810 to $870
Approximately from $780 to $860
8. A health insurer wants to know if having a nurse available to answer simple questions over a telephone hotline could cut costs by eliminating unnecessary doctor visits. Past records show the yearly average cost of doctor visits per family is around $875 with an SD of $300. They randomly select 225 families, give them access to the hotline, and record the yearly costs of their doctor visits. In this sample, they find the average yearly cost per family to be $840.
We want to test the null hypothesis that the hotline does not reduce costs, that is, average cost is $875. What would be the conclusion based on this data?
There is enough evidence to reject the null hypothesis, so we conclude that the hotline reduces costs.
There is not enough evidence to reject the null hypothesis, so we conclude that the hotline does not reduce costs.
We need more information before we can test the null hypothesis
9. Market researchers would like to know if consumers can taste the difference between a product made with low calorie oil and the same product made with regular oil. A random sample of 310 people are blindfolded and given both products to taste. Overall, 270 people correctly guess which is the low-calorie product.
Find a 95% confidence interval for the population percentage of people who can correctly guess the low-calorie product.
Approximately 84.3% to 89.9%
Approximately 83.3% to 90.9%
Approximately 81.3% to 92.9%
Approximately 76.3% to 97.9%
Market researchers would like to know if consumers can taste the difference between a product made with low calorie oil and the same product made with regular oil. A random sample of 400 people are blindfolded and given both products to taste. Overall, 230 people correctly guess which is the low-calorie product.
Is there evidence of a difference in taste of the two products?
Sample percentage of correct guesses is 1.5 standard errors above 50%, so there is no evidence of a difference in taste.
Sample percentage of correct guesses is 2.0 standard errors above 50%, so there is no evidence of a difference in taste.
Sample percentage of correct guesses is 3.0 standard errors above 50%, so there is evidence of a difference in taste.