2023 Spring Semester Exam

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2

Ch.5
Estimate the mean and standard deviation of the normal density curve in the figure:

Mean = _______ 
Standard Deviation= _______ 
Your answers should be whole numbers.

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1

Ch.5
The standard deviation of the number of puzzles subject could solve is 0.9 and the mean is 7.4 puzzles.
Which of the following is the best interpretation of the standard deviation?

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2

Ch.5
The proportion of pepperoni pizza orders on a randomly selected day at a local pizza shop is approximately normal with mean = 0.25 and standard deviation = 0.02.
Let X= the proportion of pepperoni pizza orders on a randomly selected day.

On your half sheet: 
Add the data values for standard deviations above and below the mean.

Use the Normal Distribution Curve and the 68-95-99.7 Rule to answer the following.
Hint: you should not need to use the blue chart for this problem.
a. The probability that the proportion of pepperoni pizza orders is less than 0.23= _______  

b. The probability that the proportion of pepperoni pizza orders is 
between 0.21 and 0.27 _______ write the probability as a decimal.

c. P(X> 0.29) = _______ 
d. The middle 95% of the proportion of pepperoni pizzas will fall 
between _______ and_______  

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2

Ch.5
Professional tennis player Novak Djokovic hits the ball extremely hard. His first-serve speeds follow a normal distribution with mean 112 miles per hour (mph) and
standard deviation of 6 mph.
Let X = the speed of one of Djokovic’s first serves at random, measured in miles per hour.
A first serve with a speed less than 100 miles per hour is considered “slow.”

What percent of Djokovic’s first serves are slow?

Hint: 1st calculate the z score
2nd use the z chart
Enter your answer as a decimal rounded to four places or a percent rounded to two places past the decimal point.

Required

2

Ch.5
Professional tennis player Novak Djokovic hits the ball extremely hard. His first-serve speeds follow a normal distribution with mean 112 miles per hour (mph) and
standard deviation of 6 mph.
Let X = the speed of one of Djokovic’s first serves at random, measured in miles per hour.

Calculate P(x > 120), this means find the probability that Djokovic's first serve is greater than 120 mph. Include four places past the decimal.

Hint: 1st calculate the z score,
2nd use the blue table, think about what direction you are interested in.

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2

Ch.6
A Gallup study on voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election.

Election records based on the community show that only 56% of all registered voters voted in the election.
Match the following items:

Draggable item		Corresponding Item
All registered voters		Parameter, calculated on the population
56%		Population
663 registered voters		Statistic, calculated on the sample
72%		Sample

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1

Ch.6
A polling organization wants to estimate the proportion of voters who favor a new law banning smoking in public buildings. The organization decides to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election.
The effect of this increase in sample size is to

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2

Ch.6
A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a normal distribution with mean 16.05 ounces and standard deviation 0.1 ounce. 
Assume that the machine is working properly. 

Four bottles are randomly selected and the number of ounces in each bottle is measured, this means n = 4.
What is the mean of the sampling distribution of sample means?  _______ 

What is the standard deviation of the sampling distribution of sample means?  _______ 

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2

Ch.6
The student newspaper at a large university asks an SRS of 250 undergraduates, “Do you favor eliminating the carnival from the end-of-term celebration?” In the sample, 150 of the 250 undergraduates are in favor. 
Suppose that 55% of all undergraduates favor eliminating the carnival. 
If you took a very large number of SRS's of size n = 250 from this population, the sampling distribution of the sample proportion, p, would have:
Mean =  _______ 

Standard Deviation= _______   round to three places past the decimal.

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1

Ch.6
The student newspaper at a large university asks an SRS of 250 undergraduates, “Do you favor eliminating the carnival from the end-of-term celebration?”
Suppose that 55% of all undergraduates favor eliminating the carnival.

For a sampling distribution of proportions, which of the following is closest to the probability of getting less than 50% in favor of eliminating the carnival in a random sample of size 250?

Use the Ch. 6 formula chart to calculate the z-score, then use the z chart.

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1

Ch.7
In a recent Gallup poll of randomly selected U.S. adults, 75% said they would vote for a law that imposed term limits on members of the U.S. Congress.
The poll’s margin of error was 4 percentage points at the 95% confidence level. This means that...
Hint: remember the interpretation of a confidence interval

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1

Ch.7
A 95% confidence interval for p, the proportion of all shoppers at a large grocery store who purchase cookies, is 0.236 to 0.282.
The point estimate and margin of error for this interval are:

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1

Ch.7
A quality control manager at a manufacturing plant wants to estimate the mean length of metal rods produced by a certain machine.
The manager is deciding between a 95% confidence level and a 99% confidence level. Compared to a 95% confidence interval, a 99% confidence interval will be...
Hint: read carefully, ex. a smaller risk of being incorrect is a larger confidence of being correct.

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1

Ch.7
A quality control manager at a manufacturing plant wants to estimate the mean length of metal rods produced by a certain machine.
The researcher wants to create a 95% confidence interval and is deciding between a sample of size n = 500 and a sample of size n = 1000.
Compared to using a sample size of n = 500, a 95% confidence interval based on a sample size of n = 1000 will be...

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2

Ch.7
Most people can roll their tongues, but some can’t.
Suppose we are interested in determining what proportion of people in a certain population can roll their tongues.
We test a random sample of 80 people from this population and find that 64 can roll their tongues.
Find the point estimate and margin of error for a 95% confidence interval for the true proportion of tongue rollers in this population is closest to...
Hint: 1st find p-hat
2nd calculate the margin of error, check your formula chart for Ch. 7

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7

Ch.7
Pauly’s Pizza claims that it takes 30 minutes, on average, to deliver a pizza to dorms at Nat’s college. After a long wait one night, Nat decides to test this claim. 
He randomly selects 15 dormitory residents and asks them to record the time it takes for Pauly’s to deliver the next pizza they order.
The sample mean is  x-bar= 33.8 minutes and 
the sample standard deviation is SDx = 7.72 minutes.
You will construct a 90% Confidence Interval:
n= _______ 
Degrees of freedom= _______ 
t-critical = _______ 
Margin of Error = _______    Check your Ch. 7 formula chart, round to three places past the decimal.
Point Estimate = _______ Use the sample mean.

Construct a 90% confidence interval for the true mean delivery time. Round both the upper and lower bounds to two places past the decimal point.
Lower bound:  _______                     Upper bound:  _______ 

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2

Ch. 7
Does the confidence interval in the previous question support Pauly's Pizza claim that it takes 30 minutes on average to deliver a pizza?
Select both correct answers:

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3

Ch.8
You survey selected members of a population that is approximately normally distributed and test the hypotheses
Ho: p = 0.86
Ha: p > 0.86
At the alpha = 0.05 significance level, you obtain a P-value of 0.062.
Which 3 of the following statements are true?

Required

1

Ch. 8
A fresh fruit distributor claims that only 4% of his Macintosh apples are bruised.
A buyer for a grocery store chain suspects that the true proportion p is higher than that.
She takes a random sample of 30 apples to test the null and alternative hypotheses
Ho: p = 0.04 Ha: p > 0.04

Which of the following statements about conditions for performing a one-sample z test for the population proportion is correct?
Hint: Check the conditions first.

Required

1

Ch. 8
As a construction engineer for a city, you are responsible for ensuring that the company that is providing gravel for a new road puts as much gravel in each truckload as they claim.
Each truckload is supposed to have 20 cubic meters of gravel, so you will test the hypotheses Ho: μ = 20 versus
Ha: μ < 20
at the α = 0.05 level.

Describe a Type I error in this setting.

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1

The recommended daily allowance (RDA) of calcium for women between the ages of 18 and 24 years is 1200 milligrams (mg).
Researchers who were involved in a large-scale study of women’s bone health suspected that their participants had significantly lower calcium intakes than the RDA.
To test this suspicion, the researchers measured the daily calcium intake of a random sample of 36 women from the study who fell in the desired age range.
The sample mean was 856.2 mg and the standard deviation was 306.7 mg.

Calculate the standardized test statistic for the significance test of the mean calcium intake.
Round your answer to three places past the decimal.

Required

4

Suppose that you want to perform a test of 
Ho: p = 0.9 versus 
Ha: p < 0.9. 
An SRS of size 150 from the population of interest yields 128 successes. 
Assume that the conditions for carrying out the test are met. 
The value of p-hat = _______ round to three places past the decimal.
Calculate the standardized test statistic. z=_______ 
Check the symbol in the alternative hypothesis carefully.
What is the P-value for the test statistic? _______ 
Do we reject or fail to reject the significance test? _______ enter the correct answer

2023 Spring Semester Exam

Ch.5The standard deviation of the number of puzzles subject could solve is 0.9 and the mean is 7.4 puzzles. Which of the following is the best interpretation of the standard deviation?

Ch.6A Gallup study on voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records based on the community show that only 56% of all registered voters voted in the election. Match the following items:

Ch.7A 95% confidence interval for p, the proportion of all shoppers at a large grocery store who purchase cookies, is 0.236 to 0.282. The point estimate and margin of error for this interval are:

Ch. 7Does the confidence interval in the previous question support Pauly's Pizza claim that it takes 30 minutes on average to deliver a pizza?Select both correct answers:

Ch.8You survey selected members of a population that is approximately normally distributed and test the hypotheses Ho: p = 0.86 Ha: p > 0.86 At the alpha = 0.05 significance level, you obtain a P-value of 0.062. Which 3 of the following statements are true?

Ch.5The standard deviation of the number of puzzles subject could solve is 0.9 and the mean is 7.4 puzzles. Which of the following is the best interpretation of the standard deviation?

Ch.6A Gallup study on voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records based on the community show that only 56% of all registered voters voted in the election. Match the following items:

Ch.7A 95% confidence interval for p, the proportion of all shoppers at a large grocery store who purchase cookies, is 0.236 to 0.282. The point estimate and margin of error for this interval are:

Ch. 7Does the confidence interval in the previous question support Pauly's Pizza claim that it takes 30 minutes on average to deliver a pizza?Select both correct answers:

Ch.8You survey selected members of a population that is approximately normally distributed and test the hypotheses Ho: p = 0.86 Ha: p > 0.86 At the alpha = 0.05 significance level, you obtain a P-value of 0.062. Which 3 of the following statements are true?

Ch.5
The standard deviation of the number of puzzles subject could solve is 0.9 and the mean is 7.4 puzzles.
Which of the following is the best interpretation of the standard deviation?

Ch.6
A Gallup study on voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election.

Election records based on the community show that only 56% of all registered voters voted in the election.
Match the following items:

Ch.7
A 95% confidence interval for p, the proportion of all shoppers at a large grocery store who purchase cookies, is 0.236 to 0.282.
The point estimate and margin of error for this interval are:

Ch. 7
Does the confidence interval in the previous question support Pauly's Pizza claim that it takes 30 minutes on average to deliver a pizza?
Select both correct answers:

Ch.8
You survey selected members of a population that is approximately normally distributed and test the hypotheses
Ho: p = 0.86
Ha: p > 0.86
At the alpha = 0.05 significance level, you obtain a P-value of 0.062.
Which 3 of the following statements are true?

Ch.5
The standard deviation of the number of puzzles subject could solve is 0.9 and the mean is 7.4 puzzles.
Which of the following is the best interpretation of the standard deviation?

Ch.6
A Gallup study on voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election.

Election records based on the community show that only 56% of all registered voters voted in the election.
Match the following items:

Ch.7
A 95% confidence interval for p, the proportion of all shoppers at a large grocery store who purchase cookies, is 0.236 to 0.282.
The point estimate and margin of error for this interval are:

Ch. 7
Does the confidence interval in the previous question support Pauly's Pizza claim that it takes 30 minutes on average to deliver a pizza?
Select both correct answers:

Ch.8
You survey selected members of a population that is approximately normally distributed and test the hypotheses
Ho: p = 0.86
Ha: p > 0.86
At the alpha = 0.05 significance level, you obtain a P-value of 0.062.
Which 3 of the following statements are true?