Homework: Self-Check 5.2 Save score 0 of 1 pt 5 R4 complete) HW Score: 56.67%, 2

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Homework: Self-Check 5.2 Save score 0 of 1 pt 5 R4 complete) HW Score: 56.67%, 2.83 at 5 p 7.3.29-T BE Question Help A car oompany say that the mean gas ga mleoge 21 and standard deviwionot sdam Assume he population namwy dnbute1 Which sampling distribution be used and w A normal ampang dismibution because the population is Hormu isamping disituton becsu he population is normal ind D Us 31 amping detributor because the populasaeis nama, and O E. Use a sempling denbution because n F Ute a normo samping buton becauon the papulator is normal, and o Clck to select your and hen cack Check Answer remaining

Explanation / Answer

Solution:-

We will use the t distribution becuase the popluation is normal and is unknown.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: > 24

Alternative hypothesis: < 24

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.75

DF = n - 1 = 16 - 1

DF= 15

t = (x - ) / SE

t = - 4

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Here is the logic of the analysis: Given the alternative hypothesis, we want to know whether the observed sample mean is small enough to cause us to reject the null hypothesis.

The observed sample mean produced a t statistic test statistic of - 4. We use the t Distribution Calculator to find P(t < - 4.0) = 0.00058

Interpret results. Since the P-value (0.00058) is less than the significance level (0.05), wehave to reject the null hypothesis.

From the above test we do not have suffcicient evidence to support the claim that mean mileage is atleast 24.

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