A test was conducted for two overnight mail delivery services. Two samples of identical deliveries were set up so that both delivery services were notified of the need for a delivery at the same time. The hours required to make each delivery follow. Do the data shown suggest a difference in the delivery times for the two services? Use a .05 level of significance for the test. Use Table 1 of Appendix B. Click on the datafile logo to reference the data. DATA file Service Delivery 1 2 1 24.5 28.0 2 26.0 25.5 3 28.0 32.0 4 21.0 20.0 5 18.0 19.5 6 36.0 28.0 7 25.0 29.0 8 21.0 22.0 9 24.0 23.5 10 26.0 29.5 11 31.0 30.0 What is the z-statistic (to 2 decimals)? Enter negative values as negative number, if necessary. -0.56 What is the p-value (to 4 decimals)? 0.5754 Conclude: Do not reject the null hypothesis Observe: There is not a significant difference.
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The null hypothesis (H0) is that there is no difference in the delivery times for the two services. The alternative hypothesis (H1) is that there is a difference in the delivery times. Show more…
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a. What are the null and alternate hypotheses? b. What are the test statistics? c. What are the p-values? d. Using a .05 significance level, what is your decision regarding the null hypotheses? e. Interpret the result.
Jon S.
Flying Home for the Holidays, On Time In Exercise 4.115 on page $302,$ we compared the average difference between actual and scheduled arrival times for December flights on two major airlines: Delta and United. Suppose now that we are only interested in the proportion of flights arriving more than 30 minutes after the scheduled time. Of the 1,000 Delta flights, 67 arrived more than 30 minutes late, and of the 1,000 United flights, 160 arrived more than 30 minutes late. We are testing to see if this provides evidence to conclude that the proportion of flights that are over 30 minutes late is different between flying United or Delta. (a) State the null and alternative hypothesis. (b) What statistic will be recorded for each of the simulated samples to create the randomization distribution? What is the value of that statistic for the observed sample? (c) Use StatKey or other technology to create a randomization distribution. Estimate the p-value for the observed statistic found in part (b). (d) At a significance level of $\alpha=0.01$, what is the conclusion of the test? Interpret in context. (e) Now assume we had only collected samples of size $75,$ but got essentially the same proportions (5/75 late flights for Delta and $12 / 75$ late flights for United). Repeating steps (b) through (d) on these smaller samples, do you come to the same conclusion?
Hypothesis Tests
A Closer Look at Testing
For Exercises 2 through $12,$ perform each of these steps. Assume that all variables are normally or approximately normally distributed. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Toy Assembly Test An educational researcher devised a wooden toy assembly project to test learning in 6-year-olds. The time in seconds to assemble the project was noted, and the toy was disassembled out of the child's sight. Then the child was given the task to repeat. The researcher would conclude that learning occurred if the mean of the second assembly times was less than the mean of the first assembly times. At $\alpha=0.01,$ can it be concluded that learning took place? Use the $P$ -value method, and find the $99 \%$ confidence interval of the difference in means. $$ \begin{array}{l|ccccccc}{\text { Child }} & {1} & {2} & {3} & {4} & {5} & {6} & {7} \\ \hline \text { Trial } 1 & {100} & {150} & {150} & {110} & {130} & {120} & {118} \\ \hline \text { Trial 2} & {90} & {130} & {150} & {90} & {105} & {110} & {120}\end{array} $$
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