Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-The $95 \%$ confidence interval for a collection of paired sample data is $0.0 < \mu _ { \mathrm { d } } < 3.4$ . Based on the same sample, a traditional hypothesis test fails to support the claim of $\mathrm { u } _ { \mathrm { d } } > 0$ . What can you conclude about the significance level of the hypothesis test?

Question

Construct a confidence interval for

\mu _ { \mathrm { d } }

, the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-The

95 \%

confidence interval for a collection of paired sample data is

0.0 < \mu _ { \mathrm { d } } < 3.4

. Based on the same sample, a traditional hypothesis test fails to support the claim of

\mathrm { u } _ { \mathrm { d } } > 0

. What can you conclude about the significance level of the hypothesis test?

Quizplus · Accepted Answer

Since the confidence interval for $\mu _ { \mathrm { d } }$ does not include 0, we can conclude that there is evidence to support the claim of $\mu _ { \mathrm { d } } > 0$ at the 95% confidence level. Therefore, the hypothesis test failing to support the claim of $\mathrm { u } _ { \mathrm { d } } > 0$ means that the p-value is greater than 0.05 (the significance level for a 95% confidence interval). Thus, we can conclude that $\alpha < 0.05$.

Construct a Confidence Interval For μd\mu _ { \mathrm { d } }μd​

Construct a Confidence Interval For $\mu _ { \mathrm { d } }$