What can be concluded at the the α = 0.10 level of significance?

Question

The average amount of time it takes for couples to further communicate with each other after their first date has ended is 3.53 days.  Is this average shorter for blind dates? A researcher interviewed 51 couples who had recently been on blind dates and found that they averaged 3.2 days to communicate with each other after the date was over.  Their standard deviation was 1.093 days. What can be concluded at the the  = 0.10 level of significance?

1. For this study, we should use 
2. The null and alternative hypotheses would be:     

   ?

    ?

3. The test statistic  = ? (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  

Answer 1

Ho: u = 3.53

Ha: u < 3.53

z = (3.2 - 3.53)/(1.093/sqrt(51)) = -2.156

p-value = P(z < -2.156) = 0.0154

p-value is less than alpha = 0.1, so reject Ho.