Estimating Mean and Standard Deviation

What is the formula for determining the sample size when estimating the population mean?

• n = (Z^2 * σ^2) / (E^2)

• n = (Z * σ) / (E^2)

• n = (Z^2 * σ) / (E)

• n = (Z * σ^2) / (E)

Discuss the impact of population standard deviation on the sample size calculation for estimating the population mean.

• A larger standard deviation requires a larger sample size

• A larger standard deviation requires a smaller sample size

• A larger standard deviation requires a smaller sample size

• Standard deviation has no impact on sample size calculation

Provide an example of determining the sample size for estimating the population mean using a specific formula or method.

• n = (Z^2 * σ) / (E)

• n = (Z * σ) / (E)

• n = (Z^2 * σ^2) * E

• Using the formula n = (Z^2 * σ^2) / (E^2)

What is the significance level and how does it affect the sample size calculation for estimating the population mean?

• It determines the color of the confidence interval

• It has no effect on the sample size calculation

• It is used to calculate the median instead of the mean

• It affects the sample size calculation by determining the critical value for the confidence interval.

The term "snowstorms of note" applies to all snowfalls over 6 inches. The snowfall amounts for snowstorms of note in Utica, New York, over a four-year period are as follows: 7.1, 9.2, 8.0, 6.1, 14.4, 8.5, 6.1, 6.8, 7.7, 21.5, 6.7, 9.0, 8.4, 7.0, 11.5, 14.1, 9.5, 8.6 What are the mean and SAMPLE standard deviation for these data, to the nearest hundredth?

• mean = 9.46; standard deviation = 3.74

• mean = 9.46; standard deviation = 3.85

• mean = 9.45; standard deviation = 3.74

• mean = 9.45; standard deviation = 3.85

If test scores for a class are: 100, 100, 90, 90, 80, 80, 70, 70, 60, and 60, what are the mean and sample standard deviation?

• mean = 80, stdev = 14.9

• mean = 70, stdev = 14.9

• mean = 80, stdev = 13.9

• mean = 80, stdev = 12.9

• mean = 85, stdev = 14.9

The term "snowstorms of note" applies to all snowfalls over 6 inches. The snowfall amounts for snowstorms of note in Utica, New York, over a four-year period are as follows: 7.1, 9.2, 8.0, 6.1, 14.4, 8.5, 6.1, 6.8, 7.7, 21.5, 6.7, 9.0, 8.4, 7.0, 11.5, 14.1, 9.5, 8.6 What are the mean and population standard deviation for these data, to the nearest hundredth?

• mean = 9.46; standard deviation = 3.74

• mean = 9.46; standard deviation = 3.85

• mean = 9.45; standard deviation = 3.74

• mean = 9.45; standard deviation = 3.85

Use the dataset to calculate the following summary statistics in the questions below. Report each with one decimal place.

1 , 17, 12, 20, 27, 23, 8, 5

The mean is​ ​ (a)  

The median is ​ (b)  

The skew is ​ ​ (c)  

• 14.0

• 14.5

• 13.8

• 14.01

• left

• right

• centered

A study of all the students at a small college showed a mean age of 20.7 and a standard deviation of 2.5 years.

Label both numbers with their appropriate symbol.

​ (a)   = 20.7 and ​ (b)   = 2.5

• 𝜇

• 𝜎

How does the desired confidence level influence the sample size determination for estimating the population mean?

• It only affects the margin of error but not the level of significance

• It only affects the level of significance but not the margin of error

• It affects the margin of error and the level of significance in the calculation of the sample size.

• It has no impact on the sample size determination