Calculus and Above

Calculus Questions? Ask a Mathematician for Answers ASAP

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For the problems that require...

For the problems that require a written response, please use proper English and complete sentences. Your definitions and explanations should be explicit and meaningful from a statistical viewpoint. Where appropriate, fill in the space with the required missing term or value. For the blanks that are followed by parentheses, select the best answer from within the parenthesis that follows it. For the computational problems, show all essential work, but please make use of your calculator's statistical keys. Problem #1 is worth five points, and Problems 2-11 are each worth ten points. Thus there are a total of 105 points that can be earned on this test with five of those points considered extra credit. Round all answers appropriately depending upon the type of problem; for instance z-values should be rounded to the nearest hundredth but t-values should be rounded to the nearest thousandth, etc.

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1. According to the National Automobile Dealers Association, the average price of a new car is $28,400. Nationwide the standard deviation in new car prices is $712. A random sample of 15 convertibles had a mean price of $24,300 with a standard deviation of $860 and a random sample of 12 station wagons had a mean price of $25,200 with a standard deviation of $937. Assume that the prices of convertibles and the prices of station wagons are normally distributed. It was conjectured that the variance in the prices of all convertibles is not appreciably different than the variance in the prices of all station wagons. In a test of this claim, the claim should be located in _________ (Ho, H1), the distribution that can be justifiably utilized in a test of this claim is the _______________ (chi-square, F, t, z-standard normal), and the calculate test statistic value is ________ (actually calculate the test statistic value for this test of hypothesis.)

2. A 2005 report from the Medical Association stated that the average salary of psychiatrists was $189,121 with a standard deviation of $26,975. A random sample of 64 psychiatrists was recently taken to test the claim that the average salary of psychiatrists is still $189,121, and it was found that the p-value is 0.036. Answer the following:

a) State any significance level (there is more than one correct answer) for which the appropriate conclusion would be that the current average salary of all psychiatrists is not significantly different from $189,121.

b) If using the traditional hypothesis testing procedure resulted in a decision to accept Ho and the null hypothesis turned out to actually be false, then which of the following errors could have been made: margin of error, sampling error, standard error, Type I error, Type II error?

3. A recent gasoline survey said that the national average price of gasoline is $3.67 a gallon. It was felt that gasoline in Texas was significantly lower than the national average. A survey of 8 different locations in Texas found the average price of gasoline to be $3.48 a gallon with a standard deviation of $0.19. Using a 0.05 significance level and an assumption that gasoline prices in Texas are approximately normally distributed, test this suspicion by answering parts a-d below.

a) State the null and the alternative hypotheses by filling in the blanks below.

H0: ____________ vs. H1:______________

b) The appropriate distribution to use to test this claim is the _______________ (chi-square, F, t, z-standard normal), and the critical value(s) is/are _________________.

c) The calculated test statistic value is ____________.

d) Based upon your pervious answers (don’t leave any blank blank on this test – guessing is better than nothing) the appropriate decision is to _________ (accept/fail to reject Ho, reject Ho), which indicates that the claim stated in this problem ______________ (is, is not) supported.

4. A researcher claims that the average miles per gallon (mpg) using an octane booster is higher than the average mpg without an octane booster. A random sample of five cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Data are provided below. Test this claim, using alpha=0.05, and make any necessary assumptions regarding the distribution of the variable.

Car # mpg With Booster mpg Without Booster

1 24 21

2 25 25

3 26 21

4 28 30

5 21 20

a) State the null and the alternative hypotheses by filling in the blanks below.

H0: ____________ vs. H1:______________

b) The appropriate distribution to use to test this claim is the _______________ (chi-square, F, t, z-standard normal), and the critical value(s) is/are _________________.

c) The calculated test statistic value is ____________.

d) Based upon your pervious answers the appropriate decision is to _________ (accept/fail to reject Ho, reject Ho), which indicates that the claim stated in this problem ______________ (is, is not) supported.

5. Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if there is an appreciable difference between the average price of imported wine and the average price of domestic wine. The data obtained is shown below. Use a 5% significance level to conduct this test of hypotheses.

Imported Wine Domestic Wine

= $ 8.03 = $ 7.59

s = $ 2.51 s = $ 3.26

n = 41 n = 31

a) State the null and the alternative hypotheses by filling in the blanks below.

H0: ____________ vs. H1:______________

b) The appropriate distribution to use to test this claim is the _______________ (chi-square, F, t, z-standard normal), and the critical value(s) is/are _________________.

c) The calculated test statistic value is ____________.

d) Based upon your pervious answers the appropriate decision is to _________ (accept/fail to reject Ho, reject Ho), which indicates that the claim stated in this problem ______________ (is, is not) supported.

6. A sample of 25 different payroll departments found that the employees worked an average of 310.3 days a year with a standard deviation of 23.8 days. What is the 95% confidence interval for the average days worked of all payroll departments? Assume that the distribution of days worked is approximately normally distributed. (Show your work by copying the appropriate formula from the list given at the start of this test and indicate what values you are inserting into that formula as well as stating your final answer.)

7. A real estate agent wishes to estimate the average size of homes for sale in his/her state. From a study nationwide, the mean was found to be 2515 ft2 and the standard deviation was found to be 734.87 ft2. In order to be 95% confident and accurate within 50 square feet of the true mean for this real estate agent's U.S. state, what is the minimum sample size required? (Show your work by copying the appropriate formula from the list given at the start of this test and indicate what values you are inserting into that formula as well as stating your final answer.)

8. In a study conducted by a podiatrist, it was found that 60% of 25 randomly selected women, wear dress shoes that are too small for their feet. The Academy of Orthopedic Surgeons, stated that it wants to be 95% confident and accurate within 7% of the true proportion of all women who wear dress shoes that are too small for their feet. What is the minimum sample size needed in order to meet the stated specifications? (Show your work by copying the appropriate formula from the list given at the start of this test and indicate what values you are inserting into that formula as well as stating your final answer.)

9. The Pizza Shop wanted to determine what proportion of customers would order the Tri-Pizza Special. Out of 50 customers surveyed, 15 said they would order the Tri-Pizza Special. What is the 95% confidence interval of the true proportion of all customers who would order the Tri-Pizza Special? (Show your work by copying the appropriate formula from the list given at the start of this test and indicate what values you are inserting into that formula as well as stating your final answer.)

10. It has been claimed that at University College more than 35% of the students live off campus. From a sample of 150 students, it was found that 48% live off campus. Using a significance level of 0.05, test this claim.

a) State the null and the alternative hypotheses by filling in the blanks below.

H0: ____________ vs. H1:______________

b) The appropriate distribution to use to test this claim is the _______________ (chi-square, F, t, z-standard normal), and the critical value(s) is/are _________________.

c) The calculated test statistic value is ____________.

d) Based upon your pervious answers the appropriate decision is to _________ (accept/fail to reject Ho, reject Ho), which indicates that the claim stated in this problem ______________ (is, is not) supported.

11. A cardiologist believes that the standard deviation in the systolic blood pressures of all asthma patients is below 18. A random sample of 24 asthma patients found an average systolic blood pressure of 119 with a standard deviation of 17.3. Assume the variable is normally distributed and use a significance level of 0.05 to test the doctor’s claim.

a) State the null and the alternative hypotheses by filling in the blanks below.

H0: ____________ vs. H1:______________

b) The appropriate distribution to use to test this claim is the _______________ (chi-square, F, t, z-standard normal), and the critical value(s) is/are _________________.

c) The calculated test statistic value is ____________.

d) Based upon your pervious answers the appropriate decision is to _________ (accept/fail to reject Ho, reject Ho), which indicates that the claim stated in this problem ______________ (is, is not) supported.

or

or

1. According to the National Automobile Dealers Association, the average price of a new car is $28,400. Nationwide the standard deviation in new car prices is $712. A random sample of 15 convertibles had a mean price of $24,300 with a standard deviation of $860 and a random sample of 12 station wagons had a mean price of $25,200 with a standard deviation of $937. Assume that the prices of convertibles and the prices of station wagons are normally distributed. It was conjectured that the variance in the prices of all convertibles is not appreciably different than the variance in the prices of all station wagons. In a test of this claim, the claim should be located in _________ (Ho, H1), the distribution that can be justifiably utilized in a test of this claim is the _______________ (chi-square, F, t, z-standard normal), and the calculate test statistic value is ________ (actually calculate the test statistic value for this test of hypothesis.)

2. A 2005 report from the Medical Association stated that the average salary of psychiatrists was $189,121 with a standard deviation of $26,975. A random sample of 64 psychiatrists was recently taken to test the claim that the average salary of psychiatrists is still $189,121, and it was found that the p-value is 0.036. Answer the following:

a) State any significance level (there is more than one correct answer) for which the appropriate conclusion would be that the current average salary of all psychiatrists is not significantly different from $189,121.

b) If using the traditional hypothesis testing procedure resulted in a decision to accept Ho and the null hypothesis turned out to actually be false, then which of the following errors could have been made: margin of error, sampling error, standard error, Type I error, Type II error?

3. A recent gasoline survey said that the national average price of gasoline is $3.67 a gallon. It was felt that gasoline in Texas was significantly lower than the national average. A survey of 8 different locations in Texas found the average price of gasoline to be $3.48 a gallon with a standard deviation of $0.19. Using a 0.05 significance level and an assumption that gasoline prices in Texas are approximately normally distributed, test this suspicion by answering parts a-d below.

a) State the null and the alternative hypotheses by filling in the blanks below.

H0: ____________ vs. H1:______________

b) The appropriate distribution to use to test this claim is the _______________ (chi-square, F, t, z-standard normal), and the critical value(s) is/are _________________.

c) The calculated test statistic value is ____________.

d) Based upon your pervious answers (don’t leave any blank blank on this test – guessing is better than nothing) the appropriate decision is to _________ (accept/fail to reject Ho, reject Ho), which indicates that the claim stated in this problem ______________ (is, is not) supported.

4. A researcher claims that the average miles per gallon (mpg) using an octane booster is higher than the average mpg without an octane booster. A random sample of five cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Data are provided below. Test this claim, using alpha=0.05, and make any necessary assumptions regarding the distribution of the variable.

Car # mpg With Booster mpg Without Booster

1 24 21

2 25 25

3 26 21

4 28 30

5 21 20

a) State the null and the alternative hypotheses by filling in the blanks below.

H0: ____________ vs. H1:______________

b) The appropriate distribution to use to test this claim is the _______________ (chi-square, F, t, z-standard normal), and the critical value(s) is/are _________________.

c) The calculated test statistic value is ____________.

d) Based upon your pervious answers the appropriate decision is to _________ (accept/fail to reject Ho, reject Ho), which indicates that the claim stated in this problem ______________ (is, is not) supported.

5. Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if there is an appreciable difference between the average price of imported wine and the average price of domestic wine. The data obtained is shown below. Use a 5% significance level to conduct this test of hypotheses.

Imported Wine Domestic Wine

= $ 8.03 = $ 7.59

s = $ 2.51 s = $ 3.26

n = 41 n = 31

a) State the null and the alternative hypotheses by filling in the blanks below.

H0: ____________ vs. H1:______________

b) The appropriate distribution to use to test this claim is the _______________ (chi-square, F, t, z-standard normal), and the critical value(s) is/are _________________.

c) The calculated test statistic value is ____________.

d) Based upon your pervious answers the appropriate decision is to _________ (accept/fail to reject Ho, reject Ho), which indicates that the claim stated in this problem ______________ (is, is not) supported.

6. A sample of 25 different payroll departments found that the employees worked an average of 310.3 days a year with a standard deviation of 23.8 days. What is the 95% confidence interval for the average days worked of all payroll departments? Assume that the distribution of days worked is approximately normally distributed. (Show your work by copying the appropriate formula from the list given at the start of this test and indicate what values you are inserting into that formula as well as stating your final answer.)

7. A real estate agent wishes to estimate the average size of homes for sale in his/her state. From a study nationwide, the mean was found to be 2515 ft2 and the standard deviation was found to be 734.87 ft2. In order to be 95% confident and accurate within 50 square feet of the true mean for this real estate agent's U.S. state, what is the minimum sample size required? (Show your work by copying the appropriate formula from the list given at the start of this test and indicate what values you are inserting into that formula as well as stating your final answer.)

8. In a study conducted by a podiatrist, it was found that 60% of 25 randomly selected women, wear dress shoes that are too small for their feet. The Academy of Orthopedic Surgeons, stated that it wants to be 95% confident and accurate within 7% of the true proportion of all women who wear dress shoes that are too small for their feet. What is the minimum sample size needed in order to meet the stated specifications? (Show your work by copying the appropriate formula from the list given at the start of this test and indicate what values you are inserting into that formula as well as stating your final answer.)

9. The Pizza Shop wanted to determine what proportion of customers would order the Tri-Pizza Special. Out of 50 customers surveyed, 15 said they would order the Tri-Pizza Special. What is the 95% confidence interval of the true proportion of all customers who would order the Tri-Pizza Special? (Show your work by copying the appropriate formula from the list given at the start of this test and indicate what values you are inserting into that formula as well as stating your final answer.)

10. It has been claimed that at University College more than 35% of the students live off campus. From a sample of 150 students, it was found that 48% live off campus. Using a significance level of 0.05, test this claim.

a) State the null and the alternative hypotheses by filling in the blanks below.

H0: ____________ vs. H1:______________

b) The appropriate distribution to use to test this claim is the _______________ (chi-square, F, t, z-standard normal), and the critical value(s) is/are _________________.

c) The calculated test statistic value is ____________.

d) Based upon your pervious answers the appropriate decision is to _________ (accept/fail to reject Ho, reject Ho), which indicates that the claim stated in this problem ______________ (is, is not) supported.

11. A cardiologist believes that the standard deviation in the systolic blood pressures of all asthma patients is below 18. A random sample of 24 asthma patients found an average systolic blood pressure of 119 with a standard deviation of 17.3. Assume the variable is normally distributed and use a significance level of 0.05 to test the doctor’s claim.

a) State the null and the alternative hypotheses by filling in the blanks below.

H0: ____________ vs. H1:______________

b) The appropriate distribution to use to test this claim is the _______________ (chi-square, F, t, z-standard normal), and the critical value(s) is/are _________________.

c) The calculated test statistic value is ____________.

d) Based upon your pervious answers the appropriate decision is to _________ (accept/fail to reject Ho, reject Ho), which indicates that the claim stated in this problem ______________ (is, is not) supported.

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