Sonya is paid $417.96 for 27 hours of work. taylor is paid $495.36 for 32 hours of work. which employee is paid a higher hourly
1 answer:
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Answer:
a)
b)The 99% confidence interval would be given by (0.301;0.355)
Step-by-step explanation:
1) Notation and definitions
number of permanent dwellings on the entire reservation that are traditional hogans.
random sample taken
estimated proportion of permanent dwellings on the entire reservation that are traditional hogans.
true population proportion of permanent dwellings on the entire reservation that are traditional hogans.
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
Part a
The point of estimate for p=the proportion of all permanent dwellings on the entire reservation that are traditional hogans is given by:
Part b
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 99% of confidence, our significance level would be given by and
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
The 99% confidence interval would be given by (0.301;0.355)
Using the z-distribution, it is found that the lower bound of the 99% confidence interval is given by:
d. 68.39%.
<h3>What is a confidence interval of proportions?</h3>A confidence interval of proportions is given by:
In which:
is the sample proportion.
- z is the critical value.
- n is the sample size.
In this problem, we have a 99% confidence level, hence, z is the value of Z that has a p-value of
, so the critical value is z = 2.575.
The sample size and estimate are given by:
Hence, the lower bound is given by:
Hence the lower bound is of 68.39%, which means that option D is correct.
More can be learned about the z-distribution at brainly.com/question/25890103
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