Question

Use the given information to find the number of degrees of​ freedom, the critical values xl^2 and xr^2​, and the confidence interval estimate of the standard mean. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Platelet Counts of Women 95​% ​confidence; n=25​, s=65.5.

Answer 1

The number of degrees of freedom is obtained by subtracting 1 from the sample size. The critical values xl^2 and xr^2 can be found using the chi-square distribution table. The confidence interval estimate of the population mean is calculated using the sample mean, critical value, standard deviation, and sample size. Confidence interval = (49.86, 81.14)

Step-by-step explanation:

The number of degrees of freedom in this case is n-1, where n is the sample size. So, in this case, the number of degrees of freedom is 24 (25-1=24).

The critical values xl^2 and xr^2 can be determined using the chi-square distribution table or calculator. For a 95% confidence level and 24 degrees of freedom, the critical values are approximately 37.65 and 11.07.

To calculate the confidence interval estimate of the population mean, we use the formula:
Confidence interval = sample mean ± (critical value * standard deviation / √(sample size))

Plugging in the given values, we have:
Confidence interval = 65.5 ± (11.07 * 65.5 / √(25))
Confidence interval = (49.86, 81.14)