Question 1

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a standard error of $20.If 90% and 95% confidence intervals were developed to estimate the true cost of the microwave,what similarities would they have?
A)Point estimates
B)Z-variates
C)Standard errors
D)Both "a" and "c"

Accepted Answer

Both confidence intervals would have the same point estimate (mean price of a microwave = $375) and the same standard error ($20), as these values are based on the sample data. The only difference would be the z-value used to calculate the interval, which would be slightly larger for the 95% interval than the 90% interval.

Question 2

Assuming a population standard deviation of 3 hours,what is the required sample size if the error should be less than ½ hour with a 99% level of confidence?
A)196
B)240
C)15
D)16

Accepted Answer

The formula for sample size with a known population standard deviation is:
n = (Zα/2 * σ / E) ^ 2
where:
Zα/2 = critical value for the confidence level
σ = population standard deviation
E = maximum allowable error

For a 99% level of confidence, Zα/2 = 2.576
σ = 3
E = 0.5

Substituting these values into the formula, we get:
n = (2.576 * 3 / 0.5) ^ 2
n ≈ 239.55

Since we cannot have a partial sample, we round up to the nearest whole number:
n = 240

Therefore, the required sample size is 240. Answer choice B is correct.

Question 3

If university officials say that at least 70% of the voting student population supporting the fee increase,If the 95% confidence interval is [0.75,0.85],what conclusion can be drawn based on a 95% level of confidence?
A)70% is not in the interval,need to take another sample
B)70% is not in the interval,so assume it will not be supported
C)70% is below the interval,so assume it will be supported
D)Since this was not based on population,cannot make conclusion

Accepted Answer

The entire confidence interval [0.75, 0.85] is above 70%, indicating that it is likely that at least 70% of the voting student population supports the fee increase.

Question 4

A sample of 100 students is selected from a known population of 1000 students to construct a 95% confidence interval for the average SAT score.What correction factor should be used to compute the standard error?
A)0.949
B)0.901
C)1.96
D)Cannot be determined

Accepted Answer

The correction factor, also known as the finite population correction (FPC), is used when sampling without replacement from a finite population. It is calculated as sqrt((N-n)/(N-1)), where N is the population size and n is the sample size. Here, N = 1000 and n = 100, so the FPC = sqrt((1000-100)/(1000-1)) = sqrt(900/999) ≈ 0.949.

Question 5

A survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98 with a standard error of $0.10.What is the 95% confidence interval to estimate the true cost of a gallon of milk?
A)$2.81 to $3.15
B)$2.94 to $3.02
C)$2.77 to $3.19
D)$2.95 to $3.01

Accepted Answer

The answer of A survey of 25 grocery stores revealed...

Question 6

A sample of 50 is selected from a known population of 250 elements.The population standard deviation is 15.Using the finite correction factor,what is the standard error of the sample means?
A)2.89
B)1.90
C)2.12
D)Cannot be determined

Accepted Answer

The answer of A sample of 50 is selected from...

Question 7

A survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98 with a standard error of $0.10.If 90% and 95% confidence intervals are developed to estimate the true cost of a gallon of milk,what similarities would they have?
A)Point estimates
B)t-statistics
C)Standard errors
D)Both a and c

Accepted Answer

Both the 90% and 95% confidence intervals would have the same point estimate (average price of a gallon of milk) and would use the same standard error (0.10). The only difference between the two intervals would be the t-statistic used to calculate them, since the wider interval for 95% confidence would require a larger t-statistic.

Question 8

A group of statistics students decided to conduct a survey at their university to estimate the average (mean)amount of time students spent studying per week.They sampled 554 students and found a mean of 22.3 hours per week.Assuming a population standard deviation of 6 hours,what is the 95% level of confidence?
A)[21.80,22.80]
B)[16.3,28.3]
C)[21.64,22.96]
D)[20.22,22.0]

Accepted Answer

The answer of A group of statistics students decided to...

Question 9

A pharmaceutical company wanted to estimate the population mean of monthly sales for their 250 sales people.Forty sales people were randomly selected.Their mean monthly sales was $10,000 with a population standard deviation of $1000.Construct a 95% confidence interval for the population mean.
A)[9,690.1,10,309.9]
B)[9,715.5,10,284.5]
C)[8,040,11,960]
D)[8,000,12,000]

Accepted Answer

The answer of A pharmaceutical company wanted to estimate the...

Question 10

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a standard error of $20.Assuming the population is normally distributed,what is the 99% confidence interval to estimate the true cost of the microwave?
A)$367.42 to $382.58
B)$315.00 to $415.00
C)$323.40 to $426.60
D)$335.82 to $414.28

Accepted Answer

The answer of A survey of 50 retail stores revealed...

Question 11

If 95% and 98% confidence intervals were developed to estimate the true cost of the microwave,what differences would they have?
A)Standard errors
B)Interval widths
C)Z-variates
D)Both b and c

Accepted Answer

The interval widths of the two confidence intervals would differ because the wider interval has a higher level of confidence. The z-variates for the two intervals would also differ; a 95% confidence interval would have a z-variates of ±1.96, while a 98% confidence interval would have a z-variates ±2.33. Therefore, choices B and C are correct. Standard errors would be the same for both confidence intervals since they are based on the same sample data.

Question 12

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spent studying per week.Assuming a population standard deviation of 3 hours,what is the required sample size if the error should be less than ½ hour with a 99% level of confidence?
A)196
B)240
C)15
D)16

Accepted Answer

We use the formula:
n = ((z-score * standard deviation) / margin of error)^2

To find the z-score for a 99% confidence level, we look it up in the Z-table:

From the table, we find that the z-score for a 99% confidence level is 2.576.

Substituting the known values, we get:

n = ((2.576 * 3) / 0.5)^2
n = 238.42

Rounding up to the nearest integer, we get a required sample size of 240.

Question 13

A student wanted to construct a 95% confidence interval for the average age of students in her statistics class.She randomly selected 9 students.Their average age was 19.1 years with a standard deviation of 1.5 years.What is the 95% confidence interval for the population mean?
A)[0.97,3.27]
B)[15.64,22.56]
C)[17.97,20.23]
D)[17.95,20.25]

Accepted Answer

To construct a 95% confidence interval for the population mean, we can use the formula:
CI = X̄ ± t*(s/√n)
where X̄ is the sample mean, s is the sample standard deviation, n is the sample size, and t is the t-score with n-1 degrees of freedom and a 95% confidence level.

Plugging in the given values, we get:
CI = 19.1 ± t*(1.5/√9)

From the t-table with 8 degrees of freedom and a 95% confidence level, we find that the t-score is 2.306.

Substituting this value, we get:
CI = 19.1 ± 2.306*(1.5/√9)
CI = 19.1 ± 1.22

Therefore, the 95% confidence interval for the population mean is (19.1 - 1.22, 19.1 + 1.22) or (17.88, 20.32), which is closest to choice D (17.95, 20.25).

Question 14

A student wanted to construct a 95% confidence interval for the average age of students in her statistics class.She randomly selected 9 students.Their average age was 19.1 years with a standard deviation of 1.5 years.What is the best point estimate for the population mean?
A)2.1 years
B)1.5 years
C)19.1 years
D)9 years

Accepted Answer

The best point estimate for the population mean is the sample mean, which is 19.1 years.

Question 15

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spent studying per week.Assuming a population standard deviation of 6 hours,what is the required sample size if the error should be less than ½ hour with a 95% level of confidence?
A)554
B)130
C)35
D)393

Accepted Answer

The answer of A group of statistics students decided to...

Question 16

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a standard error of $20.Assuming the population is normally distributed,what is the 95% confidence interval to estimate the true cost of the microwave?
A)$323.40 to $426.60
B)$328.40 to $421.60
C)$350.80 to $395.80
D)$369.31 to $380.69

Accepted Answer

The answer of A survey of 50 retail stores revealed...

Question 17

A sample of 25 is selected from a known population of 100 elements.What is the finite population correction factor?
A)8.66
B)75
C)0.87
D)Cannot be determined

Accepted Answer

The finite population correction factor (FPCF) is given by FPCF = sqrt[(N-n)/(N-1)] where N is the population size and n is the sample size. Therefore, FPCF = sqrt[(100-25)/(100-1)] = 0.87, so the correct answer is C.

Question 18

A group of statistics students decided to conduct a survey at their university to find the average (mean)amount of time students spent studying per week.They sampled 240 students and found a mean of 22.3 hours per week.Assuming a population standard deviation of 6 hours,what is the 99% level of confidence?
A)[21.80,22.80]
B)[16.3,28.3]
C)[21.30,23.30]
D)[20.22,22.0]

Accepted Answer

The answer of A group of statistics students decided to...

Question 19

A survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98 with a standard error of $0.10.What is the 98% confidence interval to estimate the true cost of a gallon of milk?
A)$2.73 to $3.23
B)$2.85 to $3.11
C)$2.94 to $3.02
D)$2.95 to $3.01

Accepted Answer

The answer of A survey of 25 grocery stores revealed...

Question 20

A student wanted to construct a 95% confidence interval for the average age of students in her statistics class.She randomly selected 9 students.Their average age was 19.1 years with a standard deviation of 1.5 years.What is the 99% confidence interval for the population mean?
A)[17.42,20.78]
B)[17.48,20.72]
C)[14.23,23.98]
D)[0.44,3.80]

Accepted Answer

The answer of A student wanted to construct a 95%...

Quiz 9: Estimation and Confidence Intervals

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a standard error of $20.If 90% and 95% confidence intervals were developed to estimate the true cost of the microwave,what similarities would they have?

Assuming a population standard deviation of 3 hours,what is the required sample size if the error should be less than ½ hour with a 99% level of confidence?

If university officials say that at least 70% of the voting student population supporting the fee increase,If the 95% confidence interval is [0.75,0.85],what conclusion can be drawn based on a 95% level of confidence?

A sample of 100 students is selected from a known population of 1000 students to construct a 95% confidence interval for the average SAT score.What correction factor should be used to compute the standard error?

A survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98 with a standard error of $0.10.What is the 95% confidence interval to estimate the true cost of a gallon of milk?

A sample of 50 is selected from a known population of 250 elements.The population standard deviation is 15.Using the finite correction factor,what is the standard error of the sample means?

A survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98 with a standard error of $0.10.If 90% and 95% confidence intervals are developed to estimate the true cost of a gallon of milk,what similarities would they have?

A pharmaceutical company wanted to estimate the population mean of monthly sales for their 250 sales people.Forty sales people were randomly selected.Their mean monthly sales was $10,000 with a population standard deviation of $1000.Construct a 95% confidence interval for the population mean.

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a standard error of $20.Assuming the population is normally distributed,what is the 99% confidence interval to estimate the true cost of the microwave?

If 95% and 98% confidence intervals were developed to estimate the true cost of the microwave,what differences would they have?

A student wanted to construct a 95% confidence interval for the average age of students in her statistics class.She randomly selected 9 students.Their average age was 19.1 years with a standard deviation of 1.5 years.What is the 95% confidence interval for the population mean?

A student wanted to construct a 95% confidence interval for the average age of students in her statistics class.She randomly selected 9 students.Their average age was 19.1 years with a standard deviation of 1.5 years.What is the best point estimate for the population mean?

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a standard error of $20.Assuming the population is normally distributed,what is the 95% confidence interval to estimate the true cost of the microwave?

A sample of 25 is selected from a known population of 100 elements.What is the finite population correction factor?

A survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98 with a standard error of $0.10.What is the 98% confidence interval to estimate the true cost of a gallon of milk?

A student wanted to construct a 95% confidence interval for the average age of students in her statistics class.She randomly selected 9 students.Their average age was 19.1 years with a standard deviation of 1.5 years.What is the 99% confidence interval for the population mean?