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Degrees of Freedom In general, what does 鈥渄egrees of freedom鈥 refer to? For the sample data described in Exercise 7 鈥淩equirements,鈥 find the number of degrees of freedom, assuming that you want to construct a confidence interval estimate of using the t distribution.

Short Answer

Expert verified

The degrees of freedom refer to the number of values that can be considered independent while estimating a population parameter.

The value of the degrees of freedom to estimate the mean voltage level of smartphone batteries is equal to 11.

Step by step solution

01

Given information

Referring to Exercise 7 CQQ, it is given that a sample of size 12 is selected, showing the voltage level of smartphone batteries.

02

Degrees of freedom

The number of values that can be considered independent in estimating a population parameter is called the degrees of freedom.

In other words, it is the value obtained by subtracting those number of parameters from the total number of values available that are used in the intermediate steps to compute the sample statistic.

Here, to construct the confidence interval of the mean value using the t distribution, the mean used to compute the interval is calculated from the sample values.

Thus, the sample mean (the parameter used in between the steps) is to be used to compute the confidence interval and is calculated from the available data.

Therefore, the degrees of freedom areas follows:

df=Totalnumberofvalues-Numberofparameters=n-1=12-1=11

Thus, the value of the degrees of freedom is equal to 11.

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Most popular questions from this chapter

In Exercises 1鈥3, refer to the accompanying screen display that results from the Verizon airport data speeds (Mbps) from Data Set 32 鈥淎irport Data Speeds鈥 in Appendix B. The confidence level of 95% was used.

Degrees of Freedom

a. What is the number of degrees of freedom that should be used for finding the critical value t2?

b. Find the critical value t2corresponding to a 95% confidence level.

c. Give a brief general description of the number of degrees of freedom.

Determining Sample Size. In Exercises 31鈥38, use the given data to find the minimum sample size required to estimate a population proportion or percentage.

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a. Assume that nothing is known about the percentage to be estimated.

b. Assume that a prior study conducted by the U.S Census Bureau showed that 82% of women give birth.

c. What is wrong with surveying randomly selected adult women?

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reported that they were no longer smoking. Construct the two 95% confidence intervals. Compare the results. What do you conclude?

In Exercises 1鈥3, refer to the accompanying screen display that results from the Verizon airport data speeds (Mbps) from Data Set 32 鈥淎irport Data Speeds鈥 in Appendix B. The confidence level of 95% was used

Airport Data Speeds Refer to the accompanying screen display.

a. Express the con铿乨ence interval in the format that uses the 鈥渓ess than鈥 symbol. Given that the original listed data use one decimal place, round the con铿乨ence interval limits accordingly.

b. Identify the best point estimate of and the margin of error.

c. In constructing the con铿乨ence interval estimate of , why is it not necessary to con铿乺m that the sample data appear to be from a population with a normal distribution?

In Exercises 5鈥8, use the relatively small number of given bootstrap samples to construct the confidence interval. Freshman 15: Here is a sample of amounts of weight change (kg) of college students in their freshman year (from Data Set 6 鈥淔reshman 15鈥 in Appendix B): 11, 3, 0, -2, where -2 represents a loss of 2 kg and positive values represent weight gained. Here are ten bootstrap samples: {11, 11, 11, 0}, {11, -2, 0, 11}, {11, -2, 3, 0}, {3, -2, 0, 11}, {0, 0, 0, 3}, {3, -2, 3, -2}, {11, 3, -2, 0}, { -2, 3, -2, 3}, { -2, 0, -2, 3}, {3, 11, 11, 11}. a. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the mean weight change for the population. b. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the standard deviation of the weight changes for the population.

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