Question

The average amount of time it takes for couples to further communicate with each other after their first date has ended is 3.91 days. Is this average different for blind dates? A researcher interviewed 47 couples who had recently been on blind dates and found that they averaged 3.3 days to communicate with each other after the date was over. Their standard deviation was 1.261 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: H 0 : H 1 : 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 the populaton mean is significantly different from 3.91 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 different from 3.91. The data suggest that the population mean is not significantly different from 3.91 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 different from 3.91. The data suggest the population mean is not significantly different from 3.91 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 3.91.

Answer 1

For the given set of data

The Hypotheses are:

Rejection Region:

at 0.01 level of significance Reject Ho if |Z| > Z _0.025 =2.58 Z test is used since n=47> 30.

Test Statistic:

P-Value:

Using Z score calculated above and Z table shown below the P-value for two tailed test will be 0.0009

Conclusion:

Since P-value<< 0.01 and |Z| > Z _0.0025 hence The data suggest the populaton mean is significantly different from 3.91 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 different from 3.91.

Z table: