Question

The average amount of time it takes for couples to further communicate with each other after their first date has ended is 2.61 days. Is this average shorter for blind dates? A researcher interviewed 65 couples who had recently been on blind dates and found that they averaged 2.5 days to communicate with each other after the date was over. Their standard deviation was 0.661 days. What can be concluded at the the α = 0.01 level of significance? For this study, we should use The null and alternative hypotheses would be: H0: H1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest that the population mean is not significantly less than 2.61 at α = 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 2.61. The data suggest the populaton mean is significantly less than 2.61 at α = 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 2.61. The data suggest the population mean is not significantly less than 2.61 at α = 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 2.61.

Answer 1

In this case for testing hypothesis, we have to perform  a t-test for one mean, with unknown population standard deviation.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ ≥ 2.61

Ha: μ < 2.61

(2) Test Statistics

The t-statistic is computed as follows:

Test statistics t = -1.342

(3) P-value

The p-value corresponding to t = -1.342 and degrees of freedom (df) = 65 -1 = 64 for left tailed test is 0.0922

(Obtained using online p-value calculator. Screenshot attached)

(4) Decision about the null hypothesis

Since p = 0.0922 ≥ 0.01, we reject null hypothesis

(5) Conclusion

The data suggest that the population mean is not significantly less than 2.61 at α = 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 2.61.