SOLUTION: Can someone solve these problems step by step for me. I got them wrong on my last test. ThanYou It will be greatly appreciated. Question 1 : Confidence Intervals for the Mean

Question 79661: Can someone solve these problems step by step for me. I got them wrong on my last test. ThanYou It will be greatly appreciated.
Question 1 : Confidence Intervals for the Mean
A random sample of 17 students were tested on the SAT english exam. If the mean score was 653.4 with a standard deviation of 135.457, find the 90% confidence interval for the popultation mean. Assume that the population standard deviation in unknown. Assume the scores are approximately normally distributed. Choose the appropriate distribution and state the reason(s) for your choice.Round off your answer to 1 decimal place.
Question 2 : Confidence Interval for a Population Proportion
In a random sample of 50 students enrolled in remedial math courses 21 passed the MAT test by the end of the semester.
A. Calculate the confidence interval for the population percentage of all students in remedial math courses who passed the MAT exam by the end of the semester. Use a 90% level of significance. Round off your final answer to 1 decimal place in percent.
B. If the margin of error is changed to 13.50% and the confidence level remains the same as in Part a, what is the minimum sample size required to estimate the population proportion of students who passed the MAT test? Use the proportions from Part a. Round up the sample size.
Question 3: Hypothesis Testing for the Mean
A sociologist wants to determine if the number of individuals per family unit the national average of 2.9. She interviews 31 randomly selected families in a large apartment complex and obtains a mean of 3.1 individuals per family unit with a standard deviation of 0.80. Test the claim that the mean number of individuals per family unit is less than 2.9. Use a significance level of 0.05. Assume that the population has a normal distribution and that the population standard deviation is unknown. You must decide whether to use the z-test or t-test. If you use the z-test use the P-value method.
Question 4: Confidence intervals for Variance and Standard Deviation
Suppose you are given a sample set of data consisting of 17 body temperatures, with s=1.02. Assume that body temperatures are normally distributed . Find the 95% confidence interval for the population variance 0^2. Round off to 2 decimal places.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Question 1 : Confidence Intervals for the Mean
A random sample of 17 students were tested on the SAT english exam. If the mean score was 653.4 with a standard deviation of 135.457, find the 90% confidence interval for the popultation mean. Assume that the population standard deviation in unknown. Assume the scores are approximately normally distributed. Choose the appropriate distribution and state the reason(s) for your choice.Round off your answer to 1 decimal place.
---------------------
E=z
E=1.645[32.853]=54.04
CI=(653.4-54.04,653.4+54.04)
CI=(599.36,707.44)
---------

Question 2 : Confidence Interval for a Population Proportion
In a random sample of 50 students enrolled in remedial math courses 21 passed the MAT test by the end of the semester.
A. Calculate the confidence interval for the population percentage of all students in remedial math courses who passed the MAT exam by the end of the semester. Use a 90% level of significance. Round off your final answer to 1 decimal place in percent.
E=1.645sqrt[(21/50)(19/50)]/sqrt50
E=0.093
CI=[(21/50)-0.093,(21/50)+0.093]
CI=(0.327,0.513)
=============

B. If the margin of error is changed to 13.50% and the confidence level remains the same as in Part a, what is the minimum sample size required to estimate the population proportion of students who passed the MAT test? Use the proportions from Part a. Round up the sample size.
E = z
sqrt(n)=z/E
sqrt(n)=1.645sqrt[(21/50)(19/50)]/0.135
sqrt(n)=6.014...
n=36.17
n=36 when rounded
=============
Question 3: Hypothesis Testing for the Mean
A sociologist wants to determine if the number of individuals per family unit the national average of 2.9. She interviews 31 randomly selected families in a large apartment complex and obtains a mean of 3.1 individuals per family unit with a standard deviation of 0.80. Test the claim that the mean number of individuals per family unit is less than 2.9. Use a significance level of 0.05. Assume that the population has a normal distribution and that the population standard deviation is unknown. You must decide whether to use the z-test or t-test. If you use the z-test use the P-value method.
--------
Using the z-test or the t-test pretty much depends on what text you are
using. You will have to make that decision; there is no universal agreement
on this.
---------------------------
Question 4: Confidence intervals for Variance and Standard Deviation
Suppose you are given a sample set of data consisting of 17 body temperatures, with s=1.02. Assume that body temperatures are normally distributed . Find the 95% confidence interval for the population variance 0^2. Round off to 2 decimal places.
Check this in your text book. I don't have these formulas handy.
==============
Cheers,
Stan H.

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