A sample of 352 subscribers to Wired magazine shows the mean time spent using the Internet is 13.4 hours per week, with a sample standard deviation of 6.8 hours. Find the 95 percent confidence interval for the mean time Wired subscribers spend on the Internet.
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To find the 95 percent confidence interval for the mean time Wired subscribers spend on the Internet, we can use the following formula:
Confidence interval = Sample mean ± (Critical value * Standard deviation / Square root of sample size)
First, let's determine the critical value for a 95 percent confidence level. Since the sample size is 352, we need to find the z-score that corresponds to a confidence level of 95 percent. This can be found using a standard normal distribution table or by using a statistical software. For a 95 percent confidence level, the critical value (z-score) is approximately 1.96.
Now, we can plug in the values into the formula:
Confidence interval = 13.4 ± (1.96 * 6.8 / √352)
First, let's calculate the square root of the sample size:
√352 ≈ 18.77
Now, substitute the values into the formula:
Confidence interval = 13.4 ± (1.96 * 6.8 / 18.77)
Calculating the expression:
Confidence interval ≈ 13.4 ± (1.96 * 0.362)
Now, calculate the lower and upper bounds of the confidence interval:
Lower bound = 13.4 - (1.96 * 0.362) ≈ 12.686
Upper bound = 13.4 + (1.96 * 0.362) ≈ 14.114
Therefore, the 95 percent confidence interval for the mean time Wired subscribers spend on the Internet is approximately 12.686 hours to 14.114 hours per week.
To find the 95 percent confidence interval for the mean time Wired subscribers spend on the Internet, we can use the formula:
Confidence Interval = Mean +/- (Critical Value * Standard Error)
1. Calculate the standard error:
The standard error (SE) is the standard deviation divided by the square root of the sample size.
SE = Standard Deviation / √(Sample Size)
Plugging in the given values:
SE = 6.8 / √(352)
2. Determine the critical value:
The critical value represents the number of standard deviations we need to consider for a given confidence level.
For a 95 percent confidence level, we can use a Z-score of 1.96 (which corresponds to a two-tailed test).
You can look up the critical value in a standard normal distribution table or use a statistical calculator.
3. Calculate the margin of error:
The margin of error is the critical value multiplied by the standard error.
Margin of Error = Critical Value * Standard Error
4. Calculate the lower and upper bounds of the confidence interval:
Lower bound = Mean - Margin of Error
Upper bound = Mean + Margin of Error
Now, let's plug in the values to find the confidence interval:
SE = 6.8 / √(352)
Critical Value = 1.96 (for a 95% confidence level)
Margin of Error = Critical Value * SE
Mean = 13.4
Lower bound = Mean - Margin of Error
Upper bound = Mean + Margin of Error
By substituting the values into the formulas, we can find the 95% confidence interval for the mean time Wired subscribers spend on the Internet.
95% = mean ± 1.96 SEm
SEm = SD/√n