Confidence Interval

The hypothesis testing procedure described in Null and Alternative Hypothesis simply determines whether the null hypothesis should be rejected or not. Often we would like additional information.

For example, suppose the null hypothesis is that the population mean has a fixed value μ0, i.e. the null hypothesis H0: μ = μ0. Given any sample, we would like to use the data in the sample to calculate an interval (called a confidence interval) corresponding to that sample such that 95% of such samples will produce a confidence interval which contains the the population mean μ (where α = .05, and so 95% = 1 – α); i.e. we are 95% confident that a < μ < b where a and b are the end points of the interval. Furthermore, if a < μ0 < b, then we can’t reject the null hypothesis, while if μ0b or μ0a, then we can reject the null hypothesis.

We come back to this issue several times in the website (see for example Confidence Interval for Sampling Distributions or Confidence Interval for ANOVA).

4 Responses to Confidence Interval

1. Ryan Pfab says:

I need help to complete the following portion of an assignment:
i)Test the hypotheses that the average household income in the township is greater than \$100,000.
(ii) Construct a 95% CI for the proportion of households with family history of heart disease, separately for each race. Would you say the proportion of households with history of heart disease differ by race?
(i) Formulate the null and alternative hypotheses you would use to for the test this claim.
(ii) Conduct the test and appropriately accept or reject your null hypotheses using ANOVA.
(iii) Is there any statistically significant difference in the average household income based on race?
Thanks,
Ryan

2. Busaing Benitte says:

I need help please on how to solve the following:

Deep-breathing exercise Progressive muscle relaxation Suggestive hypnosis
8 10 6
6 10 7
7 8 8
9 9 7
8 9 7
8 9 6
7 8 5
6 10 6
5 9 8
6 6 7
7 10 7
8 9 4
10 10 5
8 10 6
9 9 6
6 8 7
8 8 6
7 8 5
9 9 8
8 8 4
7 10 5
6 10 6
8 8 7
10 9 6
7 9 5

Conduct a hypothesis testing if you were comparing deep breathing exercise and progressive muscle relaxation. Show the step-by-step process of hypothesis testing:
Null and alternative hypotheses
Level of significance
Test-statistic
Critical region
Computation of test statistic and p value
Decision

Conduct a hypothesis testing if you were comparing the three interventions altogether: deep breathing exercise, progressive muscle relaxation, suggestive hypnosis. Show the step-by-step process of hypothesis testing
• Null and alternative hypotheses
• Level of significance
• Test-statistic
• Critical region
• Computation of test statistic and p value
• Decision
• Conclusion

thank you