Question

1. A nutrition laboratory randomly selected and tested 26 reduced sodium hot dogs. It was found that their average (mean) sodium content is 310 mg with the standard deviation of 54 mg. It is known that the distribution of the sodium contents in this brand of hot dogs is approximately normal. What is a t* for a 90% confidence interval for the average (mean) sodium content of this brand of hot dogs? Round your answer to 4 decimal places.

2.A nutrition laboratory randomly selected and tested 26 reduced sodium hot dogs. It was found that their average (mean) sodium content is 310 mg with the standard deviation of 54 mg. It is known that the distribution of the sodium contents in this brand of hot dogs is approximately normal. What is the standard error of x-bar in this case? Round your answer to 2 decimal places.

oximately normal. What is the standard error of x-bar in this case? Round your answer to 2 decimal places.

A) 54.00

B) 2.08

C) 10.59

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 310

sample standard deviation = s = 54

sample size = n = 26

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

a) At 90% confidence level

$\alpha$ = 1 - 90%

$\alpha$ =1 - 0.90 =0.10

$\alpha$/2 = 0.05

t$\alpha$/2,df = t_0.05,25 = 1.7081

b) SE = (s /$\sqrt$n)

  SE =  (54 /$\sqrt$26)

SE = 10.59