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Construct Confidence Intervals
Part 1
1. Explain the difference between a 95% confidence interval and a 99% confidence interval in terms of probability
a) To construct a 95% confidence interval for a population, mean µ, what is the correct critical value z*?
A 95% confidence interval implies that in the event that 100 different kinds of samples are taken into consideration and a 95% confidence interval is calculated for every sample, then roughly 95 out of the 100 confidence intervals will have the true mean value, which is µ
To construct a 95% confidence interval for a population, mean µ, the correct critical value of z* is P (-1.96 < Z < 1.96) = 0.95
b) To construct a 99% confidence interval for a population, mean µ, what is the correct critical value z*?
A 99% confidence interval implies that in the event that 100 different kinds of samples are taken into consideration and a 99% confidence interval is calculated for every sample, then roughly 99 out of the 100 confidence intervals will have the true mean value, which is µ
To construct a 99% confidence interval for a population, mean µ, the correct critical value of z* is P (-2.56 < Z < 2.56) = 0.99
2. Explain what the margin of error is and how to calculate it
Margin of error is defined as the range of values both above and below the sample statistics within a confidence interval. Therefore, the margin of error indicates the number of percentage points the outcomes will vary from the real value of the population.
The margin of error can be computed in two ways:
1. Margin of error = Critical value * Standard deviation
2. Margin of error = Critical value * Standard...
A survey of a group of students at a certain college, we call College ABC, asked: “About how many hours do you study in a week?” The mean response of the 400 students is 15.8 hours. Suppose that the study time distribution of the population is known to be normal with a standard deviation of 8.5 hours. Use the survey results to construct a 95% confidence interval for the mean study time at the College ABC.
In this case:
Population Mean X = 15.8
N = 400
Standard Deviation ? = 8.5
Therefore, 95% confidence interval for the population mean is computed as follows:
X ± 1.96 ? / ?N
= 15.8 ± 1.96 8.5 / ?400
= 15.8 ± 0.833
= (14.967, 16.633)
4. Explain the difference between a null hypothesis and an alternative hypothesis
The null hypothesis is considered to be the hypothesis of no variance or no change. The researcher makes the assumption that claim is true up until sample results specify otherwise. On the other hand, alternative hypothesis is the hypothesis that the researcher wishes to prove or authenticate. That is a statement regarding the value of a parameter that is either of a lesser amount than, bigger than, or not equal to the claimed parameter.
5. Suppose that you are testing a null hypothesis H0: µ = 10 against the alternate H1: µ ? 10. A simple random sample of 35 observations from a normal population are used for a test. What values of the z statistic are statistically significant at the ? = 0.05 level?
X ± 1.96 ? / ?N
= 10 ± 1.96 ? / ?35
6. Describe the four-step process for tests of…
References
Mendenhall, W., Beaver, R. J., & Beaver, B. M. (2012). Introduction to probability and statistics. New York: Cengage Learning.
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