Question

A used car dealer says that the true average price of a two-year-old sedan (in average condition) is less than $25000. To test the statement, you take a simple random sample of 45 cars and find the sample to have an average of $20800 with a standard deviation of $6500. Test the statement at 1% significance.
Round to the fourth.
H0 :Select an answer x̄ p̂ μ p  Select an answer = < > ≠  
HA :Select an answer x̄ p̂ μ p  Select an answer = < > ≠  
Test Statistic:
P-value:
Did something significant happen? Select an answer Significance Happened Nothing Significant Happened
Select the Decision Rule: Select an answer Reject the Null Accept the Null Fail to Reject the Null
Select an answer: is or is not  enough evidence to conclude Select an answer that the true average price of a two-year-old sedan (in average condition) is less than $25000 that the true average price of a two-year-old sedan (in average condition) is $25000

Build a 98% confidence interval and decide if you can conclude the same. Use your calculator to do this and round to the second decimal place.
( , )
Can we conclude the same as our Hypothesis Test?
Select an answer: yes or no  because the true average price of a two-year-old sedan (in average condition)

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis:H0 : μ = 25000
Alternative Hypothesis: HA: μ < 25000

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (20800 - 25000)/(6500/sqrt(45))
t = -4.3345

p value = 0

Significance Happened

Reject the Null

is enough evidence to conclude Select an answer that the true average price of a two-year-old sedan (in average condition) is less than $25000

sample mean, xbar = 20800
sample standard deviation, s = 6500
sample size, n = 45
degrees of freedom, df = n - 1 = 44

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.414

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (20800 - 2.414 * 6500/sqrt(45) , 20800 + 2.414 * 6500/sqrt(45))
CI = (18460.92 , 23139.08)

yes because the true average price of a two-year-old sedan (in average condition)is less than $25000