Question

The average amount of time it takes for couples to further communicate with each other after their first date has ended is 3.19 days. Is this average shorter for blind dates? A researcher interviewed 58 couples who had recently been on blind dates and found that they averaged 3 days to communicate with each other after the date was over. Their standard deviation was 0.639 days. What can be concluded at the  αα = 0.01 level of significance?

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

H0:H0:   ?μp ?><≠=   

H1:H1:   ?pμ ?≠=<>

3. The test statistic ? tz = (please show your answer to 3 decimal places.)
4. The p-value = (Please show your answer to 4 decimal places.)
5. The p-value is ?>≤ αα
6. Based on this, we should Select an answerfail to reject accept reject the null hypothesis.
7. Thus, the final conclusion is that
   • The data suggest that the population mean is not significantly less than 3.19 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is less than 3.19.
   • The data suggest the populaton mean is significantly less than 3.19 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is less than 3.19.
   • The data suggest the population mean is not significantly less than 3.19 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is equal to 3.19.

Answer 1

a) t-test for a population mean

b) Let denotes the  population mean time for couples who have been on a blind date to communicate with each other after the date.

g) Thus, the final conclusion is that -

The data suggest that the population mean is not significantly less than 3.19 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean time for couples who have been on a blind date to communicate with each other after the date is over is less than 3.19.