Can anyone help me develop 90% confidence intervals including lower and upper limits for each of the follwing data:
the proportion of all people- 36%
the proportion of males -the percentage is 44%
the proportion of females- the percentage is 27%
the sample size is 80
I tried to do the all and the male intervals but Im very sure im wrong.
For the all I got -0.06896 and 0.107599
for the male I got -0.0668 and 0.11571
I honeslty dont even understand how to do this? Can anyone help me ? Do I need to give more information from my data? I don't know how to do this
To calculate confidence intervals for proportions, you can use the formula:
CI = p ± Z * sqrt((p * (1-p)) / n)
where:
- CI is the confidence interval,
- p is the proportion,
- Z is the z-value corresponding to the desired confidence level,
- sqrt() represents the square root function, and
- n is the sample size.
Now, let's calculate the confidence intervals for each of the given proportions:
1. Proportion of all people (36%):
- p = 0.36 (36% expressed as a decimal)
- Z = the z-value for a 90% confidence level, which is approximately 1.645
- n = 80 (sample size)
Using the formula:
CI = 0.36 ± 1.645 * sqrt((0.36 * (1-0.36)) / 80)
Calculating the lower limit:
Lower limit = 0.36 - 1.645 * sqrt((0.36 * (1-0.36)) / 80)
Lower limit ≈ 0.36 - 1.645 * 0.056
Calculating the upper limit:
Upper limit = 0.36 + 1.645 * sqrt((0.36 * (1-0.36)) / 80)
Upper limit ≈ 0.36 + 1.645 * 0.056
Therefore, the 90% confidence interval for the proportion of all people is approximately:
Lower limit: 0.261
Upper limit: 0.459
2. Proportion of males (44%):
- p = 0.44 (44% expressed as a decimal)
- Z = 1.645
- n = 80 (sample size)
Using the formula:
CI = 0.44 ± 1.645 * sqrt((0.44 * (1-0.44)) / 80)
Calculating the lower limit:
Lower limit = 0.44 - 1.645 * sqrt((0.44 * (1-0.44)) / 80)
Lower limit ≈ 0.44 - 1.645 * 0.065
Calculating the upper limit:
Upper limit = 0.44 + 1.645 * sqrt((0.44 * (1-0.44)) / 80)
Upper limit ≈ 0.44 + 1.645 * 0.065
Thus, the 90% confidence interval for the proportion of males is approximately:
Lower limit: 0.387
Upper limit: 0.493
Similarly, you can calculate the confidence interval for the proportion of females (27%) by following the same steps.
It's important to note that I have used the Z-value for a 90% confidence level, but you can choose a different confidence level if desired.