Question

4. A researcher wishes to determine whether Toyota Corollas use more gas than Honda Civics after 10,000 miles of use. Use the computer output below to test the claim at a 1% significance level that Corollas use more gas on average than Civics (Note: we made the comparison: μcorolla - μcivic).

test stat, df, p-value, mean dif, st. error,
2.67, 44, 0.005, 4.38, 1.92

Do not reject the null; The test does not show a significant difference between the two cars.

Reject the null; The test shows the Corolla consumes more gas.

Do not reject the null; The test shows he Civic use more gas than the Corolla.

Reject the null; The test shows the Civic consumes more gas.

Do not reject the null; The test shows a significant difference between the two cars.

None of these

Answer 1

Solution:-

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

Null hypothesis: uCorolla = uCivic
Alternative hypothesis: uCorolla > uCivic

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

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

SE = 1.92
DF = 44

t = [ (x1 - x2) - d ] / SE

t = 2.67

where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of 2.67

P-value = P(t > 2.67)

Use the t-calculator to determine the p-value

P-value = 0.005

Interpret results. Since the P-value (0.005) is less than the significance level (0.01), we have to reject the null hypothesis.

Reject the null; The test shows the Corolla consumes more gas.