Question

Suppose u, and u, are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. Use the two-sample t test at significance level 0.01 to test Ho: M, - uy = -10 versus H: Uy-< -10 for the following data: m = 7, x = 114.8, 9, = 5.07, n = 7, y = 129.4, and s, = 5.33. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your p-value to three decimal places.) P-value = State the conclusion in the problem context. Reject Ho. The data suggests that the difference between mean stopping distances is less than -10. Reject Ho. The data does not suggest that the difference between mean stopping distances is less than -10. O Fail to reject Ho. The data suggests that the difference between mean stopping distances is less than -10. O Fail to reject Ho. The data does not suggest that the difference between mean stopping distances is less than -10.

Answer 1

Answer Date: 10/11/2019 To test the hypothesis is that the difference between population mean stopping distance is less than -10 at 5% significance level. The null and alternative hypothesis is, H:11-12 =-10 H:1-12<-10 The t-test statistics is, By using Excel, find t-test statistics with the help of following steps is: 1) Import the data. Select the Mega Stat from Add-Ins option. Select the Compare Two Independent Groups from Hypothesis Tests. Select data input. Select Confidence level, Test difference and alternative hypothesis. Select t-test (pooled variance). 7) Click Ok. 4)

Hypothesis Test: Independent Groups (t-test, pooled variance) Sample 1 Sample 2 114.81 129.4 mean 5.07 5.33 std. dev. 7n 12 df - 14.6000 difference (Sample 1 - Sample 2) 27.0569 pooled variance 5.2016 pooled std. dev. 2.7804 standard error of difference -10 hypothesized difference -1.65 t .0620 p-value (one-tailed, lower) From the Excel output, the t-test statistics is -1.65 |. The p-value for this test is, From the Excel output, the p-value for this test is 0.0620 Decision

The conclusion is that the p-value in this context is higher than 0.05 which is 0.0620, so the null hypothesis is fail to reject at 5% level of significance. There is insufficient evidence to indicate that the difference between population mean stopping distance is less than-10. The result is not statistically significant. The answer option is 4.