A used car dealer says that the mean price of a three-year-old sports utility ve

Question

A used car dealer says that the mean price of a three-year-old sports utility vehicle is $19,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of $19,649 and a standard deviation of $1929. Is there enough evidence to reject the claim at a-0.05? Complete parts (a) through (e) below. Assume the population is normally distributed (a) Write the claim mathematically and identify Ho and Ha Which of the following correctly states Ho and Ha? A. How-$19,000 D. Ho: -319,000 ° C. Ho :,-$19,000 Ha : -319,000 F. Ho: H $19,000 Ha: #519,000 O B. Ho : #519,000 Ha : = $19,000 Ho : 25!9,000 Ha :

Explanation / Answer

Solution:

Population Mean = $19000

Sample size = 22

Sample mean = $19649

SD = $1929

Solution(a)

Null hypothesis for this claim is

H0: Mean = $19000

Alternate hypothesis for this claim is

H1: Mean is not equal to $19000

So its answer is F.

Solution(b):

this is two tailed test so alpha/2 = 0.025

and DF = 22-1 = 21

So tcrit value can be calculated from t-table

tcrit = 2.70961

Solution:

Standardized t-tests

tStat = (Xbar - mean)/SD/sqrt(n)

tstat = (19649 - 19000)1929/(sqrt(22)

tstat = 1.5780

Solution(d):

Tstat value is not in the rejection rejection so we can not reject H0. tstat is in b/w 2.7 to -2.7 so we can not reject H0.

so its answer is A. we are failed to reject H0. because test statistic is not in the rejection region.

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