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1. (TCO 8) For the...

1. (TCO 8) For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is the claim.

A car manufacturer claims that their cars get at least 35 miles per gallon of fuel. (Points : 8)

2. (TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 25 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 26.5 minutes and the standard deviation was found to be 4 minutes. Is there evidence to reject the manager’s claim at alpha =.05? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)

3. (TCO 5) At a jewelry store, the probability for a customer to make a purchase when entering the store is 35%. We asked 25 customers enter the store whether they made a purchase or not.

(a) Is this a binomial experiment? Explain how you know.

(b) Use the correct formula to find the probability that, out of 25 customers, exactly 10 of them make a purchase. Show your calculations or explain how you found the probability.

(Points : 20)

4. (TCO 6) The monthly utility bills are normally distributed with a mean value of $150 and a standard deviation of $20.

(a) Find the probability of having a utility bill between 135 and 170.

(b) Find the probability of having a utility bill less than $135.

(c) Find the probability of having a utility bill more than $180. (Points : 20)

5. (TCO 8) A Mall manager claims that in average every customer spends $42 per a single visit to the mall. To test this claim, you took a sample of 49 customers and found the sample mean to be $39 and the sample standard deviation to be $9. At alpha = 0.05, test the Mall’s manager claim. Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)

7. (TCO 7) A company’s CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 500 products, he found 30 defective products.

(a) Find a 98% confidence interval for the true proportion of defective product. Show your calculations and/or explain the process used to obtain the interval.

(b) Interpret this confidence interval and write a sentence that explains it.

(Points : 20)

8. (TCO 2) The ages of 10 students are listed in years:{ 17,20,18,24,21,26,29,18,22,28}

(a) Find the mean, median, mode, sample variance, and range.

(b) Do you think that this sample might have come from a normal population? Why or why not? (Points : 20)

(TCO 5) It has been recorded that 10 people get killed by shark attack every year. What is the probability of having 3 or 4 people get killed by shark attack this year? (Points : 6)

0.026484

0.029253

0.018917

0.010336

(TCO 6) Assuming that the data are normally distributed with a mean of 25 and a standard deviation of 1.25, what is the z-score for a value of 27? (Points : 6)

2.30

1.60

3.10

-1.60

TCO 2) Having two types of cars called type A and type B. In observing the miles per gallon we found that both types make mean miles per gallon of 32. Car A has a standard deviation of 5 miles per gallon while car B has a standard deviation of 3 miles per gallon. Which of the two car types is more consistent in fuel consumption? (Points : 6)

Type A car because it got more fuel consumption consistency.

Type B car because it got more fuel consumption consistency.

Either car type because their average fuel consumption is the same.

Neither car type because the given information is not enough to make a decision

10. (TCO 4) A jar contains balls of four different colors; red, blue, yellow and green. The total balls are divides as 40% red, 35% blue, 20% yellow, and 5% green. If you are to select one ball at random. Find the expected value of your winning amount if the payments are set to be $0, $5, $25, $70 for red, blue, yellow and green ball respectively.

Winning amount 0 5 25 70

Probability 40% 35% 20% 5%

(Points : 6)

The expected winning amount is $25.50

The expected winning amount is $14.50

The expected winning amount is $12.25

The expected winning amount is $10.25

A car manufacturer claims that their cars get at least 35 miles per gallon of fuel. (Points : 8)

2. (TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 25 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 26.5 minutes and the standard deviation was found to be 4 minutes. Is there evidence to reject the manager’s claim at alpha =.05? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)

3. (TCO 5) At a jewelry store, the probability for a customer to make a purchase when entering the store is 35%. We asked 25 customers enter the store whether they made a purchase or not.

(a) Is this a binomial experiment? Explain how you know.

(b) Use the correct formula to find the probability that, out of 25 customers, exactly 10 of them make a purchase. Show your calculations or explain how you found the probability.

(Points : 20)

4. (TCO 6) The monthly utility bills are normally distributed with a mean value of $150 and a standard deviation of $20.

(a) Find the probability of having a utility bill between 135 and 170.

(b) Find the probability of having a utility bill less than $135.

(c) Find the probability of having a utility bill more than $180. (Points : 20)

5. (TCO 8) A Mall manager claims that in average every customer spends $42 per a single visit to the mall. To test this claim, you took a sample of 49 customers and found the sample mean to be $39 and the sample standard deviation to be $9. At alpha = 0.05, test the Mall’s manager claim. Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)

7. (TCO 7) A company’s CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 500 products, he found 30 defective products.

(a) Find a 98% confidence interval for the true proportion of defective product. Show your calculations and/or explain the process used to obtain the interval.

(b) Interpret this confidence interval and write a sentence that explains it.

(Points : 20)

8. (TCO 2) The ages of 10 students are listed in years:{ 17,20,18,24,21,26,29,18,22,28}

(a) Find the mean, median, mode, sample variance, and range.

(b) Do you think that this sample might have come from a normal population? Why or why not? (Points : 20)

(TCO 5) It has been recorded that 10 people get killed by shark attack every year. What is the probability of having 3 or 4 people get killed by shark attack this year? (Points : 6)

0.026484

0.029253

0.018917

0.010336

(TCO 6) Assuming that the data are normally distributed with a mean of 25 and a standard deviation of 1.25, what is the z-score for a value of 27? (Points : 6)

2.30

1.60

3.10

-1.60

TCO 2) Having two types of cars called type A and type B. In observing the miles per gallon we found that both types make mean miles per gallon of 32. Car A has a standard deviation of 5 miles per gallon while car B has a standard deviation of 3 miles per gallon. Which of the two car types is more consistent in fuel consumption? (Points : 6)

Type A car because it got more fuel consumption consistency.

Type B car because it got more fuel consumption consistency.

Either car type because their average fuel consumption is the same.

Neither car type because the given information is not enough to make a decision

10. (TCO 4) A jar contains balls of four different colors; red, blue, yellow and green. The total balls are divides as 40% red, 35% blue, 20% yellow, and 5% green. If you are to select one ball at random. Find the expected value of your winning amount if the payments are set to be $0, $5, $25, $70 for red, blue, yellow and green ball respectively.

Winning amount 0 5 25 70

Probability 40% 35% 20% 5%

(Points : 6)

The expected winning amount is $25.50

The expected winning amount is $14.50

The expected winning amount is $12.25

The expected winning amount is $10.25

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