Answered step-by-stepMAT 160 - Confidence Interval Practice Worksheet ZInterval Problems...
MAT 160 - Confidence Interval Practice Worksheet
ZInterval Problems
- In a study of the length of time that students require to earn bachelor's degrees, 80 students are randomly selected and they are found to have a mean of 4.8 years. Assuming that the population standard deviation is known to be 2.2 years. Construct a 95% confidence interval of the population mean.
How do you know this is a ZInterval problem?
Does the resulting confidence interval contradict the fact that 39% of students earn their bachelor's degrees in 4 years?
- The world's smallest mammal is the bumblebee bat. Such bats are roughly the size of a large bumblebee. Listed below are the weights in grams from a sample of these bats. Assuming the weights of all such bats are normally distributed and have a standard deviation of 0.30 g, construct a 95% confidence interval estimate of their mean weight.
| 1.7 | 1.6 | 1.5 | 2.0 | 2.3 |
| 1.6 | 1.6 | 1.8 | 1.5 | 1.7 |
| 2.2 | 1.4 | 1.6 | 1.6 | 1.6 |
TInterval Problems
- In a study of the effects of prenatal cocaine use on infants a sample of 190 infants found a mean weight of 2700 g and a standard deviation of 645 g. Construct a 90% confidence interval for the mean birth weight of all infants born to mothers who used cocaine.
How do you know this is a TInterval problem?
- Cardiac deaths appear to increase after heavy snow-falls. An experiment was designed to compare the cardiac demands of snow shoveling to those of an electric snow thrower. Ten subjects cleared tracts of snow using both methods. Using a shovel, the ten subjects had a mean heart rate of 175 beats per minute with a standard deviation of 15 beats per minute. The ten subjects using the snow thrower had a mean heart rate of 124 beats per minute with a standard deviation of 18 beats per minute. Heart rates are known to be normally distributed.
Construct a 95% confidence interval for the mean number of beats per minute for all people using a shovel to clear a tract of snow.
Construct a 95% confidence interval for the mean number of beats per minute for all people using an electric snow thrower to clear a tract of snow.
1-PropZInterval Problems
- An interesting and popular hypothesis is that individuals can temporarily postpone their death to survive a major holiday or important even such as a birthday. In a study of this phenomenon, it was found that in the week before and the week after Thanksgiving there were 12,000 total deaths and 6,062 of them occurred in the week before Thanksgiving. Construct a 95% confidence interval estimate of the proportion of deaths in the week before Thanksgiving to the total deaths in the week before and the week after Thanksgiving.
Based on the result, does there appear to be any indication that people can temporarily postpone their death to survive the Thanksgiving holiday?
- In a poll from March 18th, 2020 of 519 likely voters by Emerson College on which democratic candidate they prefer, 54% chose Joe Biden. Construct a 95% confidence interval for the proportion of likely voters nationwide who prefer Joe Biden.
Does a majority of the nation prefer Joe Biden as the democratic candidate?
ZInterval, TInterval, and 1-PropZInterval all mixed up
- In a survey of 1002 people, 701 said that they voted in a recent presidential election. Voting records show that 61% of eligible voters actually did vote. Find a 99% confidence interval estimate of the proportion of people who say that they voted.
Are the survey results consistent with the actual voter turnout of 61%?
- When consumers apply for credit, their credit is rated using FICO scores. Credit ratings are given below for a sample of applicants for car loans. Use the sample data to construct a 99% confidence interval for the mean FICO score of all applicants for credit. Credit ratings are known to be normally distributed.
| 661 | 595 | 548 | 730 | 791 | 678 | 672 | 491 |
| 492 | 583 | 762 | 624 | 769 | 729 | 734 | 706 |
If one bank requires a credit rating of at least 620 for a car loan, does it appear that almost all applicants will have suitable credit ratings?
Sample Size for a Mean
- Gallup, a polling company, wishes to ask Americans how much time they are spending each week online. How many subjects are needed to estimate the time if they want to find the time within 0.5 hour and with 95% confidence? Initial survey results indicate that the population standard deviation is 6.6 hours.
Sample Size for a Proportion
- A researcher for the U.S. Department of the Treasury wishes to estimate the percentage of Americans who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with 98% confidence?
If we have a prior estimate from a Harris Poll that says that 23% of the sample supported abolishing the penny, what size sample would we need using this information?
Answer & Explanation
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