Exam 10: Hypothesis Tests Involving a Sample Mean or Proportion

A portfolio manager was analyzing the price-earnings ratio for this year's performance.His boss said that the average price-earnings ratio was 20 for the many stocks,which his firm had traded,but he felt that figure was too high.The portfolio manager randomly selected a sample of 50 P/E ratios and found a mean of 18.17 and standard deviation of 4.60.Assume that the population is normally distributed and test at the 0.01 level of significance. The decision is: Because the test statistic t = 2.81 is greater than 2.33,reject H0.At the 0.01 level,the sample data suggest that the average P/E ratio for the stocks is less than 20.

(True/False)

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Question 21

Retail store A retail store claims that the average age of their customers is less than 40 years old.A sample of 50 customers had an average age of 38.7 years.Assume the population standard deviation is 12.5 years and use $\alpha$ = 0.05. -What is your conclusion?

(Short Answer)

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Question 22

In testing H0: $\mu \leq$ 120; H1: $\mu$ > 120 at the $\alpha$ = .05 level of significance,the null hypothesis is rejected.We must reach the same conclusion based on a confidence interval at the 95% confidence level.

(True/False)

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Question 23

A portfolio manager was analyzing the price-earnings ratio for this year's performance.His boss said that the average price-earnings ratio was 20 for the many stocks,which his firm had traded,but he felt that figure was too high.The portfolio manager randomly selected a sample of 50 P/E ratios and found a mean of 18.17 and standard deviation of 4.60.Assume that the population is normally distributed and test at the 0.01 level of significance. The decision rule is: Reject H₀ if the calculated t < -2.405.

(True/False)

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Question 24

The ____________________ is appropriate for hypothesis tests in which the sample standard deviation(s)is used in estimating the value of the population standard deviation ( $\text { σ }$ ).

(Short Answer)

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Question 25

Which of the following p-values will lead us to reject the null hypothesis if $\alpha$ = 0.05?

(Multiple Choice)

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Question 26

A Type II error is the probability of rejecting a true null hypothesis.

(True/False)

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Question 27

Golf A round of golf on your typical course requires at least 4.5 hours.A particular golf club claims that the average length of time to complete a round of golf on their course is less than 4.5 hours.To test this claim,the club sampled 15 golfers and recorded their time to finish their round.The sample average was 4.4 hours with a standard deviation of 0.8 hours.Assume the time to complete a round of golf is normally distributed and use $\alpha$ = 0.01. -State the null and alternative hypotheses.

(Short Answer)

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Question 28

Soft drink A soft drink dispenser is set to automatically dispense drinks and ice in 8 oz.cups.The machine is set to fill the cups with 7 1/4 oz.so that the liquid will not run over the top of the cup.The company is getting complaints that the machine is filling the cups too full and spilling over.When the machine is operating properly,only 1% of the cups will not be filled properly.The production manager conducted a one-tail hypothesis test at the 0.01 level to check the machine.A sample of 50 fills was measured. -What are the appropriate hypotheses?

(Essay)

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Question 29

Use the given information to calculate the p-value and interpret the result: H₀: $\mu$ = 20,H₁: $\mu$ > 20 $\text { σ }$ = 15,n = 50, $\bar { x }$ = 22, $\alpha$ = 0.04 p-value = Interpretation:

(Short Answer)

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Question 30

Soft drink A soft drink dispenser is set to automatically dispense drinks and ice in 8 oz.cups.The machine is set to fill the cups with 7 1/4 oz.so that the liquid will not run over the top of the cup.The company is getting complaints that the machine is filling the cups too full and spilling over.When the machine is operating properly,only 1% of the cups will not be filled properly.The production manager conducted a one-tail hypothesis test at the 0.01 level to check the machine.A sample of 50 fills was measured. -A random sample of 200 observations shows that there are 36 successes.Can we conclude at the 1% significance level that the true proportion of successes in the population is less than 24%?

(Essay)

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Question 31

A portfolio manager was analyzing the price-earnings ratio for this year's performance.His boss said that the average price-earnings ratio was 20 for the many stocks,which his firm had traded,but he felt that figure was too high.The portfolio manager randomly selected a sample of 50 P/E ratios and found a mean of 18.17 and standard deviation of 4.60.Assume that the population is normally distributed and test at the 0.01 level of significance. The correct hypotheses are: H₀: $\mu$ = 20,H₁: $\mu$ =-20.

(True/False)

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Question 32

Light Bulb Mnf. A light bulb manufacturer claims that the average life of their light bulb is more than 1000 hours.To test this claim,a sample of 32 light bulbs had an average life of 1120 hours.Assume the population standard deviation is 325 hours and use $\alpha$ = 0.02. -State the decision rule in terms of the critical value.

(Short Answer)

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Question 33

Mr.Perfection Mr.Perfection,the owner of a small unique restaurant called the Village Feed Store,is concerned with the waiting time for patrons on Sunday morning - the busiest day of the week.He is fearful that,though his establishment is extremely popular,excess waiting time will drive customers to Kenny's,a restaurant down the street.The hostess insists that customers do not have to wait more than an average of 10 minutes before being seated,but Mr.Perfection feels that the waiting time is longer.He takes a random sample of 100 customers over several Sundays.Assume that the population standard deviation $\text {σ}$ = 12 minutes,and that the significance level $\alpha$ = 0.05. -What is the decision rule in terms of the sample mean $\bar { x }$ ?

(Short Answer)

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Question 34

Soft drink A soft drink dispenser is set to automatically dispense drinks and ice in 8 oz.cups.The machine is set to fill the cups with 7 1/4 oz.so that the liquid will not run over the top of the cup.The company is getting complaints that the machine is filling the cups too full and spilling over.When the machine is operating properly,only 1% of the cups will not be filled properly.The production manager conducted a one-tail hypothesis test at the 0.01 level to check the machine.A sample of 50 fills was measured. -What is the probability that the manager will fail to reject a false H₀ if the actual population proportion of defects is 0.03? Z = $\beta$ =

(Short Answer)

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Question 35

Reducing the probability of a Type I error also reduces the probability of a Type II error.

(True/False)

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Question 36

Restaurant A restaurant claims that the average gratuity per table is $15.00.To test this claim,a sample of 18 tables was selected which had an average gratuity of $13.75 with a standard deviation of $2.60.Assume the population of gratuities is normally distributed and use $\alpha$ = 0.10. -What is your conclusion?

(Essay)

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Question 37

County Agricultural A county agricultural analyst took a sample of average annual precipitation for 50 cities.He wanted to test the null hypothesis that the average annual rainfall was at most 31.0 inches against the alternative that it was greater than 31.0 inches.Assume that the sample standard deviation was 13.76,and the sample mean was 34.74.Perform the appropriate test for the county analyst at the 0.05 level. -Calculate the test statistic and write your conclusion. Appropriate test: Test statistic = Conclusion: ______

(Short Answer)

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Question 38

Bank A bank holds the mortgage on a motel which the motel owner says has an average daily revenue of at least $2048.In the event the average is not at least $2048,the bank will ask the motel owner for additional collateral for the loan as protection against loan default.A loan officer is aware that the daily average revenue is normally distributed and randomly selects 20 days during the last six months.The sample has a mean of $2003 and standard deviation of $144.00.At the 0.01 level,is the bank loan financially sound (should the bank ask for additional collateral)? -State the null and alternative hypotheses.

(Essay)

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Question 39

Mr.Perfection Mr.Perfection,the owner of a small unique restaurant called the Village Feed Store,is concerned with the waiting time for patrons on Sunday morning - the busiest day of the week.He is fearful that,though his establishment is extremely popular,excess waiting time will drive customers to Kenny's,a restaurant down the street.The hostess insists that customers do not have to wait more than an average of 10 minutes before being seated,but Mr.Perfection feels that the waiting time is longer.He takes a random sample of 100 customers over several Sundays.Assume that the population standard deviation $\text {σ}$ = 12 minutes,and that the significance level $\alpha$ = 0.05. -State the null and alternative hypotheses. H₀: H₁:

(Essay)

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Question 40

Showing 21 - 40 of 170

Retail store A retail store claims that the average age of their customers is less than 40 years old.A sample of 50 customers had an average age of 38.7 years.Assume the population standard deviation is 12.5 years and use $\alpha$ = 0.05. -What is your conclusion?

In testing H0: $\mu \leq$ 120; H1: $\mu$ > 120 at the $\alpha$ = .05 level of significance,the null hypothesis is rejected.We must reach the same conclusion based on a confidence interval at the 95% confidence level.

The ____________________ is appropriate for hypothesis tests in which the sample standard deviation(s)is used in estimating the value of the population standard deviation ( $\text { σ }$ ).

Which of the following p-values will lead us to reject the null hypothesis if $\alpha$ = 0.05?

A Type II error is the probability of rejecting a true null hypothesis.

Use the given information to calculate the p-value and interpret the result: H₀: $\mu$ = 20,H₁: $\mu$ > 20 $\text { σ }$ = 15,n = 50, $\bar { x }$ = 22, $\alpha$ = 0.04 p-value = Interpretation:

Reducing the probability of a Type I error also reduces the probability of a Type II error.

A Preview of Business Statistics

Visual Description of Data

Statistical Description of Data

Data Collection and Sampling Methods

Probability: Review of Basic Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Estimation From Sample Data

Hypothesis Tests Involving Two Sample Means

Analysis of Variance Tests

Chi-Square Applications

Nonparametric Methods

Simple Linear Regression and Correlation

Multiple Regression and Correlation

Model Building

Models for Time Series and Forecasting

Decision Theory

Total Quality Management

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Exam 10: Hypothesis Tests Involving a Sample Mean or Proportion

Retail store A retail store claims that the average age of their customers is less than 40 years old.A sample of 50 customers had an average age of 38.7 years.Assume the population standard deviation is 12.5 years and use α\alphaα = 0.05. -What is your conclusion?

In testing H0: μ≤\mu \leqμ≤ 120; H1: μ\muμ > 120 at the α\alphaα = .05 level of significance,the null hypothesis is rejected.We must reach the same conclusion based on a confidence interval at the 95% confidence level.

The ____________________ is appropriate for hypothesis tests in which the sample standard deviation(s)is used in estimating the value of the population standard deviation ( σ \text { σ } σ ).

Which of the following p-values will lead us to reject the null hypothesis if α\alphaα = 0.05?

A Type II error is the probability of rejecting a true null hypothesis.

Use the given information to calculate the p-value and interpret the result: H0: μ\muμ = 20,H1: μ\muμ > 20 σ \text { σ } σ = 15,n = 50, xˉ\bar { x }xˉ = 22, α\alphaα = 0.04 p-value = ____________________ Interpretation: ____________________

Reducing the probability of a Type I error also reduces the probability of a Type II error.

A Preview of Business Statistics

Visual Description of Data

Statistical Description of Data

Data Collection and Sampling Methods

Probability: Review of Basic Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Estimation From Sample Data

Hypothesis Tests Involving Two Sample Means

Analysis of Variance Tests

Chi-Square Applications

Nonparametric Methods

Simple Linear Regression and Correlation

Multiple Regression and Correlation

Model Building

Models for Time Series and Forecasting

Decision Theory

Total Quality Management

Filters

Retail store A retail store claims that the average age of their customers is less than 40 years old.A sample of 50 customers had an average age of 38.7 years.Assume the population standard deviation is 12.5 years and use $\alpha$ = 0.05. -What is your conclusion?

In testing H0: $\mu \leq$ 120; H1: $\mu$ > 120 at the $\alpha$ = .05 level of significance,the null hypothesis is rejected.We must reach the same conclusion based on a confidence interval at the 95% confidence level.

The ____________________ is appropriate for hypothesis tests in which the sample standard deviation(s)is used in estimating the value of the population standard deviation ( $\text { σ }$ ).

Which of the following p-values will lead us to reject the null hypothesis if $\alpha$ = 0.05?

Use the given information to calculate the p-value and interpret the result: H₀: $\mu$ = 20,H₁: $\mu$ > 20 $\text { σ }$ = 15,n = 50, $\bar { x }$ = 22, $\alpha$ = 0.04 p-value = Interpretation: