What is a mixed number between 3 and 4
1 answer:
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Answer:
We are confident at 95% that the difference between the two proportions is between
1. -.4401 ≤ p1 - p2 ≤ -.1380
4. The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%
Step-by-step explanation:
In San Jose a sample of 73 mail carriers showed that 30 had been bitten by an animal during one week. In San Francisco in a sample of 80 mail carriers, 56 had received animal bites. Is there a significant difference in the proportions? Use a 0.05. Find the 95% confidence interval for the difference of the two proportions. Sellect all correct statements below based on the data given in this problem.
1. -.4401 ≤ p1 - p2 ≤ -.1380
2. -.4401 ≤ p1 - p2 ≤ .1380
3. The rate of mail carriers being bitten in San Jose is statistically greater than the rate San Francisco at α = 5%
4. The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%
5. The rate of mail carriers being bitten in San Jose and San Francisco are statistically equal at α = 5%
Solution to the problem
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".
represent the real population proportion for San Jose
represent the estimated proportion for San Jos
is the sample size required for San Jose
represent the real population proportion for San Francisco
represent the estimated proportion for San Francisco
is the sample size required for San Francisco
represent the critical value for the margin of error
The population proportion have the following distribution
The confidence interval for the difference of two proportions would be given by this formula
For the 95% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
We are confident at 95% that the difference between the two proportions is between
Since the confidence interval contains all negative values we can conclude that the proportion for San Jose is significantly lower than the proportion for San Francisco at 5% level.
Based on this the correct options are:
1. -.4401 ≤ p1 - p2 ≤ -.1380
4. The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%
Answer:
The 99% confidence interval is
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is
The population standard deviation is
From the question we are told the confidence level is 99% , hence the level of significance is
=>
Generally from the normal distribution table the critical value of is
Generally the margin of error is mathematically represented as
=>
Generally 95% confidence interval is mathematically represented as
=>
=>