Which is a secant of circle A?
1 answer:
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Answer:
a)
The 90% confidence interval would be given by (0.400;0.472)
b) We are confident at 90% that the true proportion of female in the Labor Force is between 0.400 and 0.472
c) Null hypothesis:
Alternative hypothesis:
For this case since the upper limit of the confidence interval is lower than 0.48 (0.472<0.48) we can conclude that the true proportion of female is actually lower than 0.48 or 48% at 10% of signficance.
Step-by-step explanation:
Part a
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by and
. And the critical value would be given by:
The estimated proportion for female is
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
The 90% confidence interval would be given by (0.400;0.472)
Part b
We are confident at 90% that the true proportion of female in the Labor Force is between 0.400 and 0.472
Part c
We need to conduct a hypothesis in order to test the claim that the true proportion is lower than 0.48:
Null hypothesis:
Alternative hypothesis:
For this case since the upper limit of the confidence interval is lower than 0.48 (0.472<0.48) we can conclude that the true proportion of female is actually lower than 0.48 or 48% at 10% of signficance.