Question 1

The federal government would like to estimate the proportion of families with no savings. The total sample size needed to construct a 95% confidence interval for the proportion of families with no savings with a margin of error equal to 6% is __________.

Accepted Answer

The answer of The federal government would like to estimate...

Question 2

If a pilot sample is not available, it is recommended to set the sample proportion equal to 0.50 to calculate the required sample size for a confidence interval for the proportion.

Accepted Answer

When no pilot sample or prior estimate of the population proportion is available, setting the sample proportion to 0.50 is recommended because it maximizes the sample size calculation, ensuring that the calculated sample size is sufficient for a wide range of actual proportions.

Question 3

The point estimate may not equal the true population mean because of the presence of sampling error.

Accepted Answer

The point estimate, such as the sample mean, may not equal the true population mean due to sampling error, which arises from natural fluctuations in the sample data.

Question 4

The critical z-score for a 98% confidence level is ________.

Accepted Answer

The answer of The critical z-score for a 98% confidence...

Question 5

Verizon Wireless would like to estimate the proportion of households that use cell phones for their phone service without a land line. A random sample of 150 households was selected and 48 relied strictly on cell phones for their service. The 95% confidence interval for the proportion based on this sample is ------- .

Accepted Answer

The 95% confidence interval for the proportion can be calculated using the formula for a confidence interval for 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 (for 95%, $z = 1.96$), and $n$ is the sample size. Here, $p = \frac{48}{150} = 0.32$, so the calculation is $0.32 \pm 1.96*\sqrt{\frac{0.32(1-0.32)}{150}}$, which gives the interval (0.257, 0.383).

Question 6

Steve's average golf score at his local course is 93.6 from a random sample of 34 rounds of golf. Assume that the population standard deviation for his golf score is 4.2. The margin of error for a 95% confidence interval around this sample mean is---------- .

Accepted Answer

The margin of error (ME) for a 95% confidence interval can be calculated using the formula: ME = Z * (σ/√n), where Z is the Z-score corresponding to the confidence level (for 95%, Z ≈ 1.96), σ is the population standard deviation, and n is the sample size. Plugging in the values: ME = 1.96 * (4.2/√34) ≈ 1.41.

Question 7

When we use the t-distribution to calculate a confidence interval, we need to assume that the population of interest follows the normal probability distribution.

Accepted Answer

The t-distribution is used when the population standard deviation is unknown and the sample size is small. In this case, we need to assume that the population of interest follows the normal probability distribution.

Question 8

The purpose of generating a confidence interval for the mean is to provide an estimate for the value of the population mean.

Accepted Answer

A confidence interval for the mean is used to estimate the range within which the true population mean is likely to fall, with a certain level of confidence.

Question 9

John Charleston owns a heating oil delivery company that services 1,540 residences. John would like to estimate the number of customers that have oil storage tanks that are less than 100 gallons in capacity. A random sample of 200 customers found that 63 had an oil tank that was less than 100 gallons. The 80% confidence interval to estimate the proportion of customers with oil tanks less than 100 gallons is______ .

Accepted Answer

The answer of John Charleston owns a heating oil delivery...

Question 10

The margin of error for a sample is dependent on the sample mean.

Accepted Answer

The margin of error for a sample is primarily dependent on the sample size and the variability of the population, not the sample mean. It is also influenced by the confidence level chosen for the interval.

Question 11

A __________ represents the width of the confidence interval between a sample mean and its upper limit or between a sample mean and its lower limit.

Accepted Answer

The margin of error represents the width of the confidence interval between a sample mean and its upper or lower limit, indicating the range within which the true population parameter is expected to lie with a certain level of confidence.

Question 12

A 100% confidence interval is more accurate than a 90% confidence interval and is therefore more preferable.

Accepted Answer

A 100% confidence interval is not necessarily more accurate; it simply covers the entire range of possible values, making it less informative about the parameter's likely value compared to a narrower interval like a 90% confidence interval.

Question 13

The confidence interval for the mean is symmetrical around the population mean.

Accepted Answer

The confidence interval for the mean is symmetrical around the sample mean, not the population mean. It is constructed based on the sample mean to estimate the range within which the population mean is likely to lie.

Question 14

The ------ confidence interval is a "workhorse" in the field of statistics and is seen far more than any other confidence level.

Accepted Answer

The 95% confidence interval is commonly used in statistics for hypothesis testing and estimating population parameters, due to its balance between precision and reliability.

Question 15

A random sample of 17 hotels in Boston had an average nightly room rate of $165.40 with a sample standard deviation of $21.70. The 90% confidence interval around this sample mean is___ .

Accepted Answer

The answer of A random sample of 17 hotels in...

Question 16

The shape of the t-distribution becomes similar to the binomial distribution as the sample size increases.

Accepted Answer

The shape of the t-distribution becomes similar to the normal distribution as the sample size increases, not the binomial distribution.

Question 17

Steve's average golf score at his local course is 92.9 from a random sample of 60 rounds of golf. Assume that the population standard deviation for his golf score is 4.2. The 99% confidence interval around this sample mean is ----- .

Accepted Answer

The answer of Steve's average golf score at his local...

Question 18

A sample proportion equal to 0.50 will require the smallest sample size to achieve a particular margin of error for a confidence interval for the proportion.

Accepted Answer

A sample proportion of 0.50 actually requires the largest sample size to achieve a particular margin of error, as it maximizes the product p(1-p), which is used in the formula for the standard error of the proportion.

Question 19

"Gamers" are described as people who regularly play video games. A random sample of 80 people was selected and 50 were found to be male. The margin of error for a 95% confidence interval for the proportion based on this sample is  -----------.

Accepted Answer

The answer of "Gamers" are described as people who regularly...

Question 20

The degrees of freedom are used to determine the critical z-score for the normal distribution when calculating a confidence interval.

Accepted Answer

Degrees of freedom are used to determine the critical value in t-distributions, not in the normal distribution (z-score) calculations. The normal distribution uses z-scores that are not dependent on degrees of freedom.

Quiz 8: Nutrition