Question

a used car dealer says that the mean price of a three - year - old sports utility vehicle is $22,000. you suspect this claim is incorrect and find that a random sample of 24 similar vehicles has a mean price of $22,873 and a standard deviation of $1972. is there enough evidence to reject the claim at \\( \alpha=0.05 \\)? complete parts (a) through (e) below. assume the population is normally distributed.
(a) write the claim mathematically and identify \\( h_{0} \\) and \\( h_{a} \\).
which of the following correctly states \\( h_{0} \\) and \\( h_{a} \\)?
a. \\( h_{0}: \mu=\\$ 22,000 \\)
\\( h_{a}: \mu>\\$ 22,000 \\)
b. \\( h_{0}: \mu \
eq \\$ 22,000 \\)
\\( h_{a}: \mu=\\$ 22,000 \\)
c. \\( h_{0}: \mu=\\$ 22,000 \\)
\\( h_{a}: \mu \
eq \\$ 22,000 \\)
d. \\( h_{0}: \mu=\\$ 22,000 \\)
\\( h_{a}: \mu<\\$ 22,000 \\)
e. \\( h_{0}: \mu>\\$ 22,000 \\)
\\( h_{a}: \mu \leq \\$ 22,000 \\)
f. \\( h_{0}: \mu \geq \\$ 22,000 \\)
\\( h_{a}: \mu<\\$ 22,000 \\)

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) is the statement being tested. The claim here is that the mean price \(\mu = 22000\). The alternative hypothesis \(H_a\) is what we might believe if the null hypothesis is rejected. Since we are just suspecting the claim is incorrect (a two - tailed test, not specifically greater than or less than), \(H_a:\mu
eq22000\).

Answer:

C. \(H_0:\mu = 22000\), \(H_a:\mu
eq22000\)