Question

A random sample of 64 observations produced a mean value of 86 and standard deviation of 4.5. The 95% confidence interval for the population mean μ is between:_________.

Answer 1

Answer: (84.876, 87.124)

Explanation:

Confidence interval for population mean if population standard deviation is unknown:

`\overline{x}\pm t_(\alpha/2)((s)/(√(n)))`

, where n= sample size

s= sample standard deviation

`\overline{x}` = sample mean

`\alpha=` significance level

`t_(\alpha/2)` = critical-t value

Given: n= 64

Degree of freedom = n-1 = 63

s= 4.5

`\overline{x}` = 86

`\alpha=` 0.05

`t_(\alpha/2)` = 1.9983

Now, the required 95% confidence interval would be:

`86\pm (1.9983)((4.5)/(√(64)))\\\\=86\pm (1.9983)((4.5)/(8))\\\\=86\pm (1.9983)(0.5625)\\\\\approx86\pm 1.1240\\\\ =(86-1.1240,\ 86+1.1240)\\\\=(84.876,\ 87.124)`

The 95% confidence interval for the population mean μ is between: (84.876, 87.124)