Question

In a survey, 26 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $37 and standard deviation of $2. Construct a confidence interval at a 80% confidence level. Give your answers to one decimal place. 36.48 * = 37.52

Answer 1

Solution :

Given that,

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = $37

sample standard deviation = s = $2

sample size = n = 26

Degrees of freedom = df = n - 1 = 26 - 1 = 25

At 80% confidence level the t is ,

$\alpha$ = 1 - 80% = 1 - 0.80 = 0.2

$\alpha$ / 2 = 0.2 / 2 = 0.1

t$\alpha$ /2,df = t0.1,25 = 1.316

At 80% confidance level of $\mu$ is

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

37 $\pm$ 1.316 * (2 / $\sqrt$ 26)

37 $\pm$ 0.5

(36.5 , 37.5)