# Finding the Confidence Interval for Mean Number of Hours

5. A researcher wants to estimate the mean number of hours (mu) ; children watch television per day. A sample of 38 children is taken. The sample mean is 6.8 hours with a sample standard deviation of 1.1 hours.

a. Find the 90% confidence interval for mean (mu).

b. Find the 95% confidence interval for mean (mu).

#### Solution Preview

...or M .

Confidence interval = 90%.

Therefore, significance level = 0.10 = 1-0.9.

Z at the 0.1 level of significance 2 tailed test = 1.6449.

sx=standard error of mean=s/square root of n= 0.1784 = ( 1.1 /square root of 38).

z*sx= 0.2935 =1.6449 x 0.1784.

Confidence interval = sample mean ±z*sx = 6.80 ± 0.2935.

Upper confidence limit= X bar+z*sx = 7.0935 ...