Question 1

A 95% confidence interval implies that about 95 out of 100 similarly constructed intervals will include the _____________ being estimated.

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The answer of A 95% confidence interval implies that about...

Question 2

The interval within which a population parameter is expected to lie is called a __________.

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The answer of The interval within which a population parameter...

Question 3

A survey of an urban university (population of 25,450) showed that 750 of 1,100 students sampled attended a home football game during the season. Using the 99% level of confidence, what is the confidence interval for the proportion of students attending a football game?
A)[0.767, 0.814]
B)[0.655, 0.705]
C)[0.644, 0.716]
D)[0.680, 0.681]

Accepted Answer

To find the confidence interval for the proportion, we will use the formula:
sample proportion +/- z-score * standard error of the proportion
where sample proportion = 750/1100 = 0.682, z-score for 99% confidence level = 2.576 and standard error of proportion = sqrt((0.682*0.318)/1100) = 0.017
Plugging in the values, we get:
0.682 +/- 2.576*0.017
The confidence interval comes out to be [0.767, 0.814]. Therefore, the best choice is (A).

Question 4

A(n) _________ estimate states the range within which a population parameter probably lies.

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The answer of A(n) _________ estimate states the range within...

Question 5

A survey of households in a small town showed that in 850 of 1,200 sampled households, at least one member attended a town meeting during the year. Using the 99% level of confidence, what is the confidence interval for the proportion of households represented at a town meeting?
A)[0.674, 0.742]
B)[0.655, 0.705]
C)[0.665, 0.694]
D)[0.679, 0.680]

Accepted Answer

The confidence interval for the proportion can be calculated using the formula for the confidence interval of a proportion: $p \pm Z \sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion, $Z$ is the Z-score corresponding to the confidence level, and $n$ is the sample size. Here, $p = \frac{850}{1200}$, $n = 1200$, and for a 99% confidence level, $Z \approx 2.576$. Plugging these values into the formula gives a confidence interval that matches choice A.

Question 6

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

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

Question 7

A sample mean is a _______________ estimate of the population mean.

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The answer of A sample mean is a _______________ estimate...

Question 8

Making generalized statements about a population based on sample information is called _________________.

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The answer of Making generalized statements about a population based...

Question 9

Assuming a normal population with a known population standard deviation, the z statistic for a 90% confidence interval would be ____.

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The answer of Assuming a normal population with a known...

Question 10

For a distribution of sample means with a known population standard deviation, about _____ percent of the sample means are within three standard errors of population mean.

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The answer of For a distribution of sample means with...

Question 11

A survey of 25 grocery stores revealed that the mean price of a gallon of milk was $2.98, with a standard error of $0.10. If 90% and 95% confidence intervals were developed to estimate the true cost of a gallon of milk, what similarities would they have?
A)Both have the same confidence level
B)Both use the same t statistic
C)Both use the same z statistic
D)Both use the same point estimate of the population mean

Accepted Answer

Both confidence intervals would use the same point estimate of the population mean, which is $2.98 in this case. The confidence level and the statistic used (z or t) would differ based on the confidence level specified, but the point estimate remains constant across different confidence intervals.

Question 12

When estimating a population mean with a confidence interval, a smaller margin of error requires a _________ sample size.

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The answer of When estimating a population mean with a...

Question 13

For a distribution of sample means with a known population standard deviation, about _____ percent of the sample means are within one standard error of population mean.

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The answer of For a distribution of sample means with...

Question 14

Other things being equal, a smaller sample size would result in a wider confidence interval because the standard error of the mean is ______________.

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The answer of Other things being equal, a smaller sample...

Question 15

The probability that an interval estimate includes the population parameter is called the _____________.

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The answer of The probability that an interval estimate includes...

Question 16

A survey of households in a small town showed that in 500 of 1,200 sampled households, at least one member attended a town meeting during the year. Using the 95% level of confidence, what is the confidence interval for the proportion of households represented at a town meeting?
A)[0.417, 0.427]
B)[0.389, 0.445]
C)[0.400, 0.417]
D)[0.417, 0.445]

Accepted Answer

To find the confidence interval for the proportion of households represented at a town meeting, we can use the formula:
Confidence Interval = sample proportion ± (critical value) x (standard error)
where:
- The sample proportion is 500/1200 = 0.417.
- The critical value for a 95% level of confidence and a two-tailed test is 1.96.
- The standard error can be calculated as the square root of [(sample proportion x (1- sample proportion)) / sample size]:
SE = √[(0.417 x 0.583) / 1200] ≈ 0.0188

Plugging these values into the formula, we get:
Confidence Interval = 0.417 ± (1.96 x 0.0188)
Confidence Interval = [0.381, 0.453]

Therefore, the best choice is B, which is the only option that contains the correct confidence interval (with some rounding).

Question 17

A survey of an urban university (population of 25,450) showed that 750 of 1,100 students sampled attended a home football game during the season. Using the 90% level of confidence, what is the confidence interval for the proportion of students attending a football game?
A)[0.7510, 0.8290]
B)[0.6569, 0.7031]
C)[0.6659, 0.6941]
D)[0.6795, 0.6805]

Accepted Answer

The answer of A survey of an urban university (population...

Question 18

For a sampling distribution of means with a known population standard deviation, ______% of the means would be between ±1.96 standard errors.

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The answer of For a sampling distribution of means with...

Question 19

To calculate the sample size required to estimate a population mean, we must know or estimate the ______________ of the population distribution.

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The answer of To calculate the sample size required to...

Question 20

Assuming a normal population with a known population standard deviation, the z statistic for a 99% confidence interval would be ______.

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The answer of Assuming a normal population with a known...

Quiz 9: Estimation and Confidence Intervals