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 = p̂ ± Z * √( p̂(1-p̂) / n )
where:
CI represents the confidence interval
p̂ is the proportion (expressed as a decimal)
Z is the critical value from the standard normal distribution corresponding to the desired confidence level
n is the sample size
Let's calculate the confidence intervals for each proportion step by step:
1. Proportion of all people (36%):
p̂ = 0.36
n = 80
The critical value for a 90% confidence level is Z = 1.645 (you can find this value from a standard normal distribution table)
Using the formula:
CI = 0.36 ± 1.645 * √(0.36*(1-0.36) / 80)
CI = 0.36 ± 0.1074
CI = (0.2526, 0.4674)
Therefore, the confidence interval for the proportion of all people is (0.2526, 0.4674).
2. Proportion of males (44%):
p̂ = 0.44
n = 80
Again, the critical value for a 90% confidence level is Z = 1.645.
Using the formula:
CI = 0.44 ± 1.645 * √(0.44*(1-0.44) / 80)
CI = 0.44 ± 0.1149
CI = (0.3251, 0.5549)
Thus, the confidence interval for the proportion of males is (0.3251, 0.5549).
3. Proportion of females (27%):
p̂ = 0.27
n = 80
Z = 1.645 (same as before)
Using the formula:
CI = 0.27 ± 1.645 * √(0.27*(1-0.27) / 80)
CI = 0.27 ± 0.1054
CI = (0.1646, 0.3754)
Hence, the confidence interval for the proportion of females is (0.1646, 0.3754).
Please note that these calculations assume that the sample is representative of the population and that the data follows a binomial distribution. Also, it's always a good idea to double-check your calculations and consult with a statistician to ensure accuracy.