(a) The 95% confidence interval for mean stage IV sleep is between 44.41 and 51.59.
We are 95% confident that the true mean stage IV sleep is between 44.41 and 51.59.
(b) The hypothesis being tested is:
H0: µ = 50
Ha: µ < 50
The p-value is 0.1345.
Since the p-value (0.1345) is greater than the significance level (0.05), we cannot reject the null hypothesis.
Therefore, we cannot conclude that the true mean stage IV sleep is less than 50 minutes.
(c) Yes, the confidence interval can be used. Since the confidence interval is above 50 minutes, we cannot conclude that the true mean stage IV sleep is less than 50 minutes.
50.00 | hypothesized value |
48.00 | mean 1 |
14.00 | std. dev. |
1.79 | std. error |
61 | n |
60 | df |
-1.116 | t |
.1345 | p-value (one-tailed, lower) |
44.41 | confidence interval 95.% lower |
51.59 | confidence interval 95.% upper |
3.59 | margin of error |
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