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Ch 16 & 17 Review Problems

Last updated over 4 years ago
20 questions
4

When rolling two fair dice, the probability of getting a total of 7 is p=1/6.
We plan to roll them 200 times.



What is the Expected Proportion of 7's we might observe? E(X=p)
Round your answer to three places past the decimal.

4

When rolling two fair dice, the probability of getting a total of 7 is p=1/6.
We plan to roll them 200 times.
What is the standard deviation of sample proportions? SD(X=p)


To be the most accurate, DO NOT round until the very end of your calculations. This means use (1/6) for the proportion of the sample.
At the end of your calculations, round your answer to three places past the decimal.

4

When rolling two fair dice, the probability of getting a total of 7 is p=1/6.
We plan to roll them 200 times.
What is the 95% Confidence Interval of sample proportions?

1. Calculate the number of success you expect to have (round to a whole number).
2. Use your TI-84 calculator. Stats, Test, 1-PropZInt
3. Round the values to three places past the decimal point.
List your values inside parenthesis, separated by a comma and space.
Ex. (0.123, 0.456)

4

When rolling two fair dice, the probability of getting a total of 7 is p=1/6.
We plan to roll them 200 times.
What is the Margin of Error for the 95% confidence interval?
Remember: The margin of error is half the distance of the confidence interval.

4

A computer printout summarizes the proportion of cars produced in Japan. Based on a random sample of 125 autos it gives the z-interval for the sample proportion with 95% Confidence:

What is the sample proportion of Japanese cars that was found in this sample?
Hint: the sample proportion is at the center of the 95% confidence interval.

4

Using a computer to simulate games of Scrabble, researcher Charles Robinove found that the letter 'A' appeared in 54% of the hands (this is the proportion).
He said his study had a margin of error of + or - 10%.

If this is true, give the 95% confidence interval for the proportion of A's you can expect in a hand in Scrabble.

Use parenthesis and a comma to show the values.
Ex. (0.23, 0.45)

4

A traffic study mounted a radar gun along a section of rural interstate highway where the traffic was moving smoothly, and found that 243 out of 355 cars were exceeding the posted speed limit by at least 5 miles per hour.
What is the sample proportion? (p hat)

Round to three places past the decimal.

4

A traffic study mounted a radar gun along a section of rural interstate highway where the traffic was moving smoothly, and found that 243 out of 355 cars were exceeding the posted speed limit by at least 5 miles per hour.
Estimate the variability in such sample proportions by finding SE(P hat).
Use the rounded p-hat value from #7 to find q-hat.
Hint:

Round your answer to three places past the decimal.

4

A traffic study mounted a radar gun along a section of rural interstate highway where the traffic was moving smoothly, and found that 243 out of 355 cars were exceeding the posted speed limit by at least 5 miles per hour.
Find the 95% confidence interval for this sample proportion using your TI-84 calculator.
Stat, Test, 1-PropZInt.

Round the values to three places past the decimal point.
List the values inside parenthesis, separated by a comma and space.
Ex. (0.123, 0.456)

4

A traffic study mounted a radar gun along a section of rural interstate highway where the traffic was moving smoothly, and found that 243 out of 355 cars were exceeding the posted speed limit by at least 5 miles per hour.
Create a 90% confidence interval using your TI-84 calculator.
Stat, Test, 1-PropZInt.

Round the values to three places past the decimal point.
List the values inside parenthesis, separated by a comma and space.
Ex. (0.123, 0.456)

4

Consider the difference in the two confidence intervals found in #9 & 10.
Check the two statements below that are true.

4

Same scenario: A traffic study mounted a radar gun along a section of rural interstate highway where the traffic was moving smoothly, and found that 243 out of 355 cars were exceeding the posted speed limit by at least 5 miles per hour.
Suppose you wanted to estimate the proportion of cars exceeding the speed limit and have a margin of error only 1/3 as large as the study above.
How many cars' speeds would you need to measure for your study? (this is your sample size)
Hint: -remember 'n' is under the radical in the denominator when calculating the Std Dev.
-what is done to the denominator of 1/3 to find the factor for the new 'n' under the radical

4

Ch 17 Review is from this point on.
An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Thecompany must sell those machines at a drastically reduced price, the goal is to keep the level of damaged machines below 2%.
One day an inspector randomly checks 60 washers and find that 5 of them have been damaged. Is this strong evidence that the warehouse is failing to meet the company goal?

First calculate is the sample proportion that the inspector found. Do not round your answer.

Second calculate the standard deviation for that sample, using the given proportion. Do not round.

Third calculate the z-score to determine if the sample proportion is statistically significant.


Round your answer AT THE END of your calculations to three places past the decimal.
This is the most accurate answer.

4

Using the information from #13, is this strong evidence that the warehouse is failing to meet the company goal
And
Can they test a hypothesis? HInt: check assumptions and conditions.
Choose two correct answers so that both questions are answered.

4

A garden center wants to store leftover seed packets of vegetable seeds for sale the following spring, but the center is concerned that the seeds may not germnate at the same rate a year later. The packets claim a germination rate of 92%.
Give the null and alternative hypotheses that will be tested.
Ex.
Be careful to use a subscript for the null and alternative H, use the mini keyboard at the right.
I will be checking answers to mark correct if I see you have entered the correct answer.

4

A garden center wants to store leftover seed packets of vegetable seeds for sale the following spring, but the center is concerned that the seeds may not germnate at the same rate a year later. The packets claim a germination rate of 92%.
The manager finds a seed packet, plants the seed as a test to see how many grow and finds that 171 out of 200 seeds sprout.

Calculate the z-score for this proportion, use your TI-84 calculator to find the 1-Proportion Z-Test:
Stat, Test, 1-PropZTest.

Enter both: the sample proportion(p hat), and the z-score in this order.
Separated by a comma and space.
Ex. 0.564, 2.143
Round your answer to three places past the decimal.

4

A garden center wants to store leftover seed packets of vegetable seeds for sale the following spring, but the center is concerned that the seeds may not germnate at the same rate a year later. The packets claim a germination rate of 92%.
The manager finds a seed packet, plants the seed as a test to see how many grow and finds that 171 out of 200 seeds sprout.
Do we have strong evidence that the seeds lose viability during a year in storage?

4

A company is criticized because only 13 of the 43 people in executive-level positions are women. The company explains that although this proportion is lower than it might wish, it's not surprising given that only 40% of its employees are women.
Write the null and alternative hypothesis.
Ex.
Make sure to use the mini keyboard and subscripts for the null and alternative hypotheses.
Keep 2 decimal places for the proportions.

4

A company is criticized because only 13 of the 43 people in executive-level poistions are women. The company explains that although this proportion is lower than it might wish, it's not surprising given that only 40% of its employees are women.
FInd the z-score for this sample to decide if the null hypothesis or the alternative hypothesis is true.

Perform a 1-Proportion Z-Test, use your TI-84 Calculator: stat, test, 1-PropZTest.

Round your answer to three places past the decimal.

4

A company is criticized because only 13 of the 43 people in executive-level poistions are women. The company explains that although this proportion is lower than it might wish, it's not surprising given that only 40% of its employees are women.
Based on the z-score from #19, do you think the company is justly criticized?