Question

A shoe company is interested in estimating the average amount customers spent at their new store in a mall. A sample of 25 customers produced a mean spending of RM150 and with standard deviation of RM20. A 95% confidence interval for the true mean is:

A. RM150 ± 164.80 C. RM150 ± 8.26 B. RM150 ± 8.24 D. RM150 ± 165.12

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = RM150

sample standard deviation = s = RM20

sample size = n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

At 95% confidence level the t is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

t_{$\alpha$ /2,df} = t_0.025,24 = 2.064

At 95% confidence level of $\mu$ is

$\bar x$$\pm$ t_{$\alpha$/2,df} * (s /$\sqrt$n)

150 $\pm$ 2.064 * (20 / $\sqrt$ 25)

RM150 $\pm$ 8.26

option C.