The average amount of time it takes for couples to furthercommunicate with each other after their first date has ended is3.19 days. Is this average shorter for blind dates? A researcherinterviewed 58 couples who had recently been on blind dates andfound that they averaged 3 days to communicate with each otherafter the date was over. Their standard deviation was 0.639 days.What can be concluded at the  αα = 0.01 level ofsignificance?

1. For this study, we should use Select an answer t-test for apopulation mean z-test for a population proportion
2. The null and alternative hypotheses would be:

H0:H0:   ?μp ?><≠=   

H1:H1:   ?pμ ?≠=<>

1. The test statistic ? tz = (please show your answer to 3 decimalplaces.)
2. The p-value = (Please show your answer to 4 decimalplaces.)
3. The p-value is ?>≤ αα
4. Based on this, we should Select an answerfail to reject acceptreject the null hypothesis.
5. Thus, the final conclusion is that
   • The data suggest that the population mean is notsignificantly less than 3.19 at αα = 0.01, sothere is statistically insignificant evidence to conclude that thepopulation mean time for couples who have been on a blind date tocommunicate with each other after the date is over is less than3.19.
   • The data suggest the populaton mean issignificantly less than 3.19 at αα = 0.01, sothere is statistically significant evidence to conclude that thepopulation mean time for couples who have been on a blind date tocommunicate with each other after the date is over is less than3.19.
   • The data suggest the population mean is notsignificantly less than 3.19 at αα = 0.01, sothere is statistically significant evidence to conclude that thepopulation mean time for couples who have been on a blind date tocommunicate with each other after the date is over is equal to3.19.