Stats 10.1 - 10.2 Practice Quiz

A 90% confidence interval for the true mean price, in dollars, of a bouquet of red roses from all U.S. flower shops is calculated to be (24.48, 32.68). Which of the following is a correct interpretation of the interval?

• 90% of all red rose bouquets cost between $24.48 and $32.68.

• We are 90% confident that the true mean price of all red rose bouquets in the U.S. is between $24.48 and $32.68.

• There is a 90% chance that the true mean price of all red rose bouquets in the U.S. is between $24.48 and $32.68.

• We are 90% confident that the true mean price of all red rose bouquets in the U.S. is $28.58, which is the center of the interval.

• We are 90% confident that the true mean price of all red rose bouquets in the U.S. from a different sample would be between $24.48 and $32.68.

A random sample of 30 rotisserie chickens from the deli counter of a grocery store is selected and weighed. A 95 percent confidence interval for the true mean weight of all rotisserie chickens sold at this deli counter, in kilograms, is given by (0.74, 0.95). Which of the following statements is true?

• The mean weight of all rotisserie chickens from this deli counter will be between 0.74 kg and 0.95 kg, 95% of the time.

• 95% of all rotisserie chickens from this deli counter weigh between 0.74 kg and 0.95 kg.

• 95% of all samples of 30 rotisserie chickens from this deli counter will result in a mean weight between 0.74 kg and 0.95 kg.

• 95% of all random samples of 30 rotisserie chickens from this deli counter would produce a 95% confidence interval that captures the true mean weight of rotisserie chickens.

• Of the 30 rotisserie chickens in the sample, at least 28 of them weighed between 0.74 kg and 0.95 kg.

A quality control manager at a new manufacturing plant wants to estimate the mean diameter of the bolts produced in the plant. A random sample of 60 bolts is selected and measured. The shape of the dotplot showing the 60 diameters of the bolts is approximately normal. Because the plant is new, no historical data on the variability of the diameters is available. Which of the following best explains why the manager should use a t-interval, rather than a z-interval, to make this estimate?

• The number of bolts in the sample is too small.

• The sample mean is being used to estimate the population mean.

• The sample standard deviation will be used to estimate the population standard deviation.

• The 60 bolts represent less than 10% of all bolts produced at the plant.

• The bolts were measured on a specific day, rather than across a longer time period.

Read the situation in the picture:

Which of the following could explain why the margin of error for Sample 2 is larger than the margin of error for Sample 1?

• The mean number of years is greater for Sample 2 than for Sample 1.

• The number of people in Sample 2 is greater than the number of people in Sample 1.

• The number of people in Sample 2 is less than the number of people in Sample 1.

• The number of people in Sample 2 is approximately equal to the number of people in Sample 1.

• The standard deviation of Sample 2 is less than the standard deviation of Sample 1.

Researchers conducted a study to estimate the mean number of dreams recalled by participants after exposure to a specific aromatherapy treatment. In a random sample of 50 participants, the mean number of dreams recalled was found to be 3.6, with a standard deviation of 1.2.

Calculate a 90% confidence interval for the true mean number of dreams recalled by all individuals who undergo the same aromatherapy treatment.

• (3.315, 3.885)

• (3.430, 3.770)

• (1.584, 5.616)

• (0.345, 2.055)

• (3.259, 3.941)

The Elo rating system is used to rank chess players’ skill levels, with an Elo score of 2,500 or above representing Grandmasters. Trey selects a random sample of 100 players from chess.com and calculates an average Elo rating of 1,090 for the sample, with a standard deviation of 320.

Construct and interpret a 90% confidence interval for the true mean Elo rating of all players on chess.com.

Which of the following is correct for the first C: CHOOSE

• one-sample t-interval for μ at 90% confidence level

• one-sample z-interval for μ at 90% confidence level

• two-sample t-interval for μ₁-μ₂ at 90% confidence level

• one-sample t-test for μ at α = 0.05.

• one-sample t-interval for p at 90% confidence level

The Elo rating system is used to rank chess players’ skill levels, with an Elo score of 2,500 or above representing Grandmasters. Trey selects a random sample of 100 players from chess.com and calculates an average Elo rating of 1,090 for the sample, with a standard deviation of 320.

Construct and interpret a 90% confidence interval for the true mean Elo rating of all players on chess.com.

Check all of the following that is correct for the second C: CHECK

• Random is met: the 100 players were randomly selected

• 10% is met: 100 < 0.10(all players on chess.com)

• 10% condition not met

• normal/large sample is met by the central limit theorem: 100 > 30

• normal/ large sample is met because population distribution is approximately normal.

The Elo rating system is used to rank chess players’ skill levels, with an Elo score of 2,500 or above representing Grandmasters. Trey selects a random sample of 100 players from chess.com and calculates an average Elo rating of 1,090 for the sample, with a standard deviation of 320.

Construct and interpret a 90% confidence interval for the true mean Elo rating of all players on chess.com.

The correct interval is (1036.9, 1143.1)

Which of the following is the correct was to show work for the 3rd C: CALCULATE

The Elo rating system is used to rank chess players’ skill levels, with an Elo score of 2,500 or above representing Grandmasters. Trey selects a random sample of 100 players from chess.com and calculates an average Elo rating of 1,090 for the sample, with a standard deviation of 320.

Construct and interpret a 90% confidence interval for the true mean Elo rating of all players on chess.com.

Which of the following interpretation for the confidence interval (1036.9, 1143.1).

• We are 90% confident that the interval from 1036.9 to 1143.1 captures the true mean Elo rating of all players at chess.com.

• 90% of the chess players on chess.com will have an Elo ranking above 1036 and below 1144

The Elo rating system is used to rank chess players’ skill levels, with an Elo score of 2,500 or above representing Grandmasters. Trey selects a random sample of 100 players from chess.com and calculates an average Elo rating of 1,090 for the sample, with a standard deviation of 320.

The 90% confidence interval is (1036.9, 1143.1).

Trey’s friend Beck claims that the mean Elo rating on chess.com is greater than 1,100. Based on the confidence interval, is there convincing statistical evidence to support Beck's claim? Explain.

• No, since 1100 is contained in the interval, it is plausible the true mean Elo rating on Chess.com is 1100 or less.

• Yes, since 1100 is contained in the interval we have convincing evidence that the mean Elo rating is greater than 1100.