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

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