Question

In: Statistics and Probability

Please calculate the 90% Confidence Interval for the population slope in the following scenario. Suppose that...

Please calculate the 90% Confidence Interval for the population slope in the following scenario. Suppose that you collected data to determine the relationship between the amount of time a person spends online as an independent variable and the amount of money a person spends online as the dependent variable. Use the following data for questions 6, 7, 8, 9, & 10. The regression equation is = 24 + 10.1x, where x represents the number of hours a person spends online and represents the predicted amount of money that person spends online. Sample size is 6.

SSE is 300

SSR is 900

SST is 1200

Standard deviation of the sampling distribution of the sample intercept is 9.54

Standard deviation of the sampling distribution of the sample slope is 3.16

Expert Solution

Answer:-

Given ,

x = the amount of time a person spends online

y= the amount of money a person spends online

The given regression equation is,

Here given that ,

sample size n=6

SSE=300

SSR=900

SST=1200

Let as the Standard deviation of the sampling distribution of the sample intercept and,

as the Standard deviation of the sampling distribution of the sample slope

Then the 90% Confidence Interval for the population slope is given as follows,

$[Slope-t_{\alpha/2}, _(_n_-_2_)*\sigma_{slope}, Slope+t_{\alpha/2}, _(_n_-_2_)*\sigma_{slope}]$

But Slope=10.1

$t_{\alpha/2}, _(_n_-_2_)=t_{\alpha/2}, _(_6_-_2_)= 2.131847$

This valus can be obtained from t-probability table or using R-software. R-command for it is >qt(0.95,4)

Thus,

Then the 90% Confidence Interval for the population slope is,

orchestra answered 1 year ago

For the following PAIRED OBSERVATIONS, calculate the 90% confidence interval for the population mean mu_d: A...

For the following PAIRED OBSERVATIONS, calculate the 90% confidence interval for the population mean mu_d: A = {12.16, 15.65, 12.58, 12.75}, B = {6.02, 8.95, 5.70, 6.22}.

Determine a 95% confidence interval for the population slope. What are the values in this confidence...

Determine a 95% confidence interval for the population slope. What are the values in this confidence interval tell you? Be specific X Y 1870 3.38 1330 1.16 1760 1.58 1520 2.65 1300 1.98 1520 2.39 1640 2.49 1490 2.81 1300 2.95 1360 1.69 1940 3.49 1730 2.8 1790 2.95 1780 3.8 1730 2.64 1380 2.36 1580 3.1 1900 1.96 1640 3.08 1540 2.24 1350 2.59 1380 2.43 1780 1.95 1700 2.07 1610 2.34 1720 3.59 2070 3.59 1210 2.12 1720...

Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the...

Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line. Lower bound: ? (Round to four decimal places as needed.) Upper bound:? (Round to four decimal places as needed.) (d) What is the mean rate of return for the company stock if the rate of return of the index is 3.15%? The mean rate of return for the company stock if the rate of return of the index is 3.15%...

Calculate the 99%, 95%, and 90% confidence interval for the following information. Identify how these confidence...

Calculate the 99%, 95%, and 90% confidence interval for the following information. Identify how these confidence intervals are similar and how they are different. Explain why. (70 points) x̄ = 55 s = 15 n = 101 The 99% Confidence Interval: The 95% Confidence Interval: The 90% Confidence Interval: Similarities: Differences: Why?

Assuming that the population is normally distributed, construct a 90 % confidence interval for the population...

Assuming that the population is normally distributed, construct a 90 % confidence interval for the population mean, based on the following sample size of n equals 5. 1, 2, 3, 4, and 29 In the given data, replace the value 29 with 5 and recalculate the confidence interval. Using these results, describe the effect of an outlier (that is, an extreme value) on the confidence interval, in general.

1) The following is a 90% confidence interval for a population proportion, p: CI = (0.26,...

1) The following is a 90% confidence interval for a population proportion, p: CI = (0.26, 0.54). What margin of error, ME, was used to construct this interval? Give your answer to 2 decimal places. 2)The following is a 90% confidence interval for a population proportion, p: CI = (0.26, 0.54). Find the sample proportion used in the construction of this interval. Give your answer to 2 decimal places. 3)The following is a 90% confidence interval for a population proportion,...

A 90% confidence interval for a population mean, μ, is given as (21.73, 24.64). This confidence...

A 90% confidence interval for a population mean, μ, is given as (21.73, 24.64). This confidence interval is based on a simple random sample of 41 observations. Calculate the sample mean and standard deviation. Assume that all conditions necessary for inference are satisfied. Use the t- distribution in any calculations.

Assuming that the population is normally distributed, construct a 90% confidence interval for the population mean...

Assuming that the population is normally distributed, construct a 90% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range. Sample A: 1 1 4 4 5 5 8 8 Sample B: 1 2 3 4 5 6 7 8 a. Construct a 90% confidence interval for the population mean for sample A b. Construct a 90% confidence interval...

Assuming that the population is normally distributed, construct a 90% confidence interval for the population mean,...

Assuming that the population is normally distributed, construct a 90% confidence interval for the population mean, based on the following sample size of n=7. 1, 2, 3, 4, 5 6, and 24 Change the number 24 to 7 and recalculate the confidence interval. Using these results, describe the effect of an outlier (that is, an extreme value) on the confidence interval.

this question, but calculate the 90% confidence interval for the coefficient for cable by hand (but...

this question, but calculate the 90% confidence interval for the coefficient for cable by hand (but use the SE from the software output) and do the test whether age and number of TVs should be dropped by hand (use ANVOA table to get p-value and confirm with software). The data in the table below contains observations on age, sex (male = 0, female = 1), number of television sets in the household, cable (no = 0, yes = 1), and...