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[answered] Mario the marriage celebrant is interested in investigating


Mario the marriage celebrant is interested in investigating the average age at which people who attended university get married. A sample of 45 married couples who attended university have been randomly selected and the age at which they married was recorded. The sample mean age of marriage was calculated as 28 years old. It is known that the population standard deviation of age of marriage for all people is equal to 11 years. It is assumed that this standard deviation will also apply specifically to the age of marriage for people who attended university.

Calculate the upper and lower bounds of the 95% confidence interval for the mean age of marriage for people who attended university. You may find this?standard normal table?useful. Give your answers in years to 2 decimal places.

a)Upper bound =??years old

b)Lower bound =??years old



As a stock analyst, your boss, Jerry, has asked you to compile some information on stock of Southern Infrastructure Corporation including a 95% confidence interval for the mean daily return that he needs to include in a report to senior management. He says that he is also not sure exactly what a 95% confidence interval means and would like you to add an explanation.

You have been following the share price of Southern Infrastructure Corporation and have recorded the daily return (as a percentage) for the last 120 days. The data is presented here:

Download the data

0.642 0.927 0.657 0.44 0.057 0.407 1.612 1.007 1.407 1.671 0.442 -0.885
1.047 0.061 0.068 0.801 0.818 1.703 0.334 0.738 -1.132 1.491 0.489 0.292
-0.314 0.346 1.967 -0.015 1.241 -0.416 0.94 -0.95 -0.81 1.641 0.506 1.914
0.849 0.946 0.505 1.662 -0.112 -0.554 0.199 3.248 1.004 0.717 0.467 0.749
1.863 1.602 -0.419 1.644 -0.944 1.242 0.059 -0.176 1.76 0.693 2.283 0.379
0.532 0.438 1.301 0.293 0.181 0.606 1.376 1.425 0.92 -0.417 0.048 1.178
-0.486 0.334 0.956 0.086 0.835 0.816 -0.095 2.322 -0.058 -0.846 -0.898 1.199
1.066 -0.616 0.145 0.161 -0.224 2.528 0.273 0.195 -0.27 1.587 2.229 1.244
0.673 1.713 0.718 1.467 -0.586 0.833 -0.408 0.879 1.645 1.502 0.661 0.479
0.232 -0.531 1.134 0.482 0.668 0.984 1.536 1.12 -0.566 1.152 0.347 -0.396

Historically, the standard deviation in daily return for this stock is 0.8%.

Complete the report to your boss. Give your numeric answers to 3 decimal places.

Sent: December 3, 2016 11:10 AM
To: Jerry Kendall
Subject: Southern Infrastructure Corp. stock info

Dear Jerry,

Here are the results gathered from the collected data:

Assuming a population standard deviation in daily return of 0.8%, the 95% confidence interval for the mean daily return is:

a)?? ? ??

b)This means that

approximately 95% of sample means will be within the interval given above
using a process that gives correct results in 95% of cases, the population mean daily return is within the interval given above
the population mean daily return is definitely within the interval given above
on approximately 95% of days in a given period the stock makes a return within the interval given above




WMB is a car manufacturer. The company is trying to estimate the cost of building a particular car part. Specifically, the company would like to construct a 90% confidence interval for the mean cost of building this part. For the purposes of constructing the interval, the company is assuming a particular value for the population standard deviation in this cost.

You were dozing in the meeting and so you didn't hear what this assumed value for the population standard deviation is. However, you did hear the following information: If the margin of error on the confidence interval is to be $3.43, then a sample size of 110 items is required to construct an interval this precise.

You also remember hearing the boss say that the company could easily afford to collect a sample this large. In fact, in the interests of getting a more precise estimate, the company can afford an even larger sample. A quick decision was made to shrink the margin of error to $2.93. However all other parameters of the situation are to remain the same.

Based on this information, calculate the required sample size to construct a confidence interval with this smaller margin of error. Round your answer up to the nearest whole number.

Required sample size =?



1) Sample mean ?xbar? = 28

 

Population standard deviation ??? = 11

 

Sample size ?n? = 45

 

Z score = 1.96 at 95% confidence level

 

Upper bound = xbar + Z score * ?/?n

 

= 28 + 1.96 * 11...

 


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