A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60?
a) No, and we are 90% sure of it.
b) No. The proportion is 54.17%.
c) Maybe. 0.60 is a believable value of the population proportion based on the information above.
d) Yes, and we are 90% sure of it.
a) No, and we are 90% sure of it.
b) No. The proportion is 54.17%.
c) Maybe. 0.60 is a believable value of the population proportion based on the information above.
d) Yes, and we are 90% sure of it.
Since you are already given the values for the confidence interval, take those values, add them together and divide by 2. This will be the proportion of the sample used to generate the interval. A 90% interval means that you can be 90% sure that the population proportion is contained within that interval.
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The correct answer is a) No, and we are 90% sure of it.
To explain why, we need to understand how confidence intervals work. A confidence interval is used to estimate a population parameter, such as the proportion of females in this case, based on a sample. The interval (0.438, 0.642) is a 90% confidence interval, which means that if we were to repeat the sampling process multiple times, we would expect 90% of the intervals to contain the true population proportion.
To determine if the population proportion of females is equal to 0.60, we need to check if this value falls within the confidence interval. In this case, 0.60 does not fall within the interval (0.438, 0.642), so we can conclude that the population proportion is not equal to 0.60.
Furthermore, it is important to note that confidence intervals provide a range of possible values for the population parameter, but they do not guarantee that the true value falls within that range. The interval (0.438, 0.642) suggests that the population proportion of females could be anywhere within that range, but it does not imply that the true proportion is exactly at the center of the interval (i.e., 0.54).
Therefore, the correct answer is a) No, and we are 90% sure of it, as the population proportion of females is not equal to 0.60 according to the given confidence interval.