Question

Show Introinstructions In a survey, 10 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $35 and standard deviation of $18. Construct a confidence interval at a 98% confidence level 023 Give your answers to one decimal place. S Interpret your confidence interval in the context of this problem 10/16 Box 1: Enter your answer as an integer or decimal number. Examples: 3.4 5.5172 Enter ONE for Does Not Exist. oo for Infinity Box 2: Enter your answer as an integer or decimal number. Examples: 3.-4,5.5172 Enter ONE for Does Not Exist, oo for Infinity Box 3: Enter your answer as text. This question is not automatically graded Points possible Petit forume Submit TAGG

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 35

sample standard deviation = s = 18

sample size = n = 10

Degrees of freedom = df = n - 1 = 10-1 = 9

At 98% confidence level

$\alpha$ = 1-0.98% =1-0.98 =0.02

$\alpha$/2 =0.02/ 2= 0.01

t$\alpha$/2,df = t_{0.01,9= 2.82}

t_{$\alpha$ /2,df} = 2.82

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 2.82 * (18 / $\sqrt$ 10)

Margin of error = E = 16.05

The 98% confidence interval estimate of the population mean is,

$\bar x$$\pm$E

35 $\pm$ 16.05

19.0 < $\mu$ < 51.0

(19.0,51.0)