Question

The average amount of time it takes for couples to further communicate with each other after their first date has ended is 2.01 days. Is this average different for blind dates? A researcher interviewed 68 couples who had recently been on blind dates and found that they averaged 2 days to communicate with each other after the date was over. Their standard deviation was 0.291 days. What can be concluded at the the αα = 0.10 level of significance?

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

H0: _________________  

H1:___________________

3. The test statistic: z or t =  (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 ≤ or > α
6. Based on this, we should: reject, accept, or fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean is not significantly different from 2.01 at αα = 0.10, 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 2.01.
   • The data suggest the populaton mean is significantly different from 2.01 at αα = 0.10, 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 2.01.
   • The data suggest the population mean is not significantly different from 2.01 at αα = 0.10, 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 2.01.

Answer 1

using minitab

enterdata>stat>basic stat>1 sample t
One-Sample T
Descriptive Statistics

N   Mean   StDev   SE Mean   95% CI for μ
68   2.0000   0.2910   0.0353   (1.9296, 2.0704)
μ: mean of Sample
Test

Null hypothesis   H₀: μ = 2.01
Alternative hypothesis   H₁: μ ≠ 2.01
T-Value   P-Value
-0.283   0.7778

a) we use t -test (since sigma unknown)

b)Null hypothesis   H₀: μ = 2.01
Alternative hypothesis   H₁: μ ≠ 2.01

c) t= -0.283

p value = 0.7778

we failed to reject null hypothesis.

The data suggest that the population mean is not significantly different from 2.01 at αα = 0.10, 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 2.01.