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 the αα = 0.01 level of significance?

1. For this study, we should use Select an answert-test for a population meanz-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 rejectacceptreject 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

Part a

Answer: t-test for population mean

Part b

H₀: µ = 3.19

H_a: µ < 3.19

Part c

t = (Xbar - µ)/[S/sqrt(n)]

By using given data, we have

t = (3 – 3.19)/[0.369/sqrt(58)]

t = -2.2645

Part d

P-value = 0.0137 > α = 0.01

Part f

Fail to reject the null hypothesis

Part g

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.