1. Use the first table of \"Measured Values\" for the following: For the sample
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Question
1. Use the first table of "Measured Values" for the following: For the sample mean and 95% confidence interval in the final row (Day 33), find the Margin of Error for each of the two groups Calculate the sample Standard Error for each of the two groups Find the Point Estimate and Standard Error for the difference in the means between the two groups Construct the null and alternative hypotheses for whether the treatment group had improved outcomes that were statistically significant Decide whether to reject the previous null hypothesis at the 95% level Decide whether to reject the null hypothesis at the 99% significance level a. b. c. d. e. f. Measured Values Acupuncture Control E- 1.96 Participants Analyzed [Units: Participants] 38 41 Change in Crying Time Per 24 Hour Period Units: Minutes crying time pr 24 hour] Mean (95% Confidence Interval) 220 212 Day 1 and 2-baseline (183 to 241) (195 to 245) IS Con 230 186Explanation / Answer
Part a
For the acupuncture group, 95% confidence interval is given as below:
Lower limit = 195
Upper limit = 245
Mean = 220
Lower limit = Mean – margin of error
195 = 220 – margin of error
Margin of error = 220 – 195 = 25
Margin of error = E = 25
Now, we have to find margin of error for control group. The 95% confidence interval is given as bleow:
Lower limit = 183
Upper limit = 241
Mean = 212
Lower limit = Mean – margin of error
183 = 212 - margin of error
Margin of error = 212 – 183 = 29
Part b
We have to find SE for given two groups.
For acupuncture group,
Margin of error = 25
Critical value Z for 95% is given as 1.96
Margin of error = Z*SE
SE = Margin of error / Z
SE = 25/1.96
SE = 12.7551
For control group,
Margin of error = 29
Critical value Z for 95% is given as 1.96
Margin of error = Z*SE
SE = Margin of error / Z
SE = 29/1.96
SE = 14.79592
Part c
Point estimate for difference in means = X1bar – X2bar
Point estimate for difference in means = 220 – 212
Point estimate for difference in means = 8
We have to find the SD for both groups.
For acupuncture group,
SE = 12.7551
n = 38
SE = SD/sqrt(n)
SD = SE*sqrt(n)
SD = 12.7551*sqrt(38)
SD = 78.62772
For control group,
SE = 14.79592
n = 41
SD = SE*sqrt(n)
SD = 14.79592*sqrt(41)
SD = 94.74011
Standard error for difference in means is given as below:
SE = sqrt[(S1^2/n1)+(S2^2/n2)]
SE = sqrt((78.62772*78.62772/38)+( 94.74011*94.74011/41))
SE = 19.53489
Standard error = 19.53489
Part d
Null hypothesis: H0: There is no any statistically significant difference exists between the treatment group and control group.
Alternative hypothesis: H0: There is a positive difference exists between the treatment group and control group.
H0: µacu. - µcontrol = 0
Ha: µacu. - µcontrol > 0
This is an upper tailed test.
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