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# Confidence Interval & Sample Size

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Could someone please share some knowledge on these questions. Needed to verify answers checking whether I do understand the concept thoroughly.

File Attached with t-Distribution and Chi-Square Distribution charts.

A Company surveys 32 randomly selected employees and ask the number spent working at home after hours during a week. The results as shown below:
10 5 0 8
0 3 4 4
2 3 8 1
4 1 7 5
7 6 2 1
0 5 7 5
10 5 3 6
6 2 2 3

Using Excel, construct a 90% confidence interval for the mean hours worked.
90% confidence interval: __________ +/- ________

The weights (in ounces) of 12 randomly sampled cakes as shown in the table below.
17 10 15 14
16 12 16 13
20 11 17 18
Using Excel, constructed a 98% confidence interval using a t-distribution for the mean weight.
98% confidence interval: _________+/- __________

In a survey of 942 musicians, 715 said they began playing an instrument while in elementary school.
Using Excel, construct a 90% confidence interval for the proportion of the musicians who began playing an instrument while in elementary school.
90% confidence interval: _________ +/- __________

A restaurant wants to estimate the average number of customer who ask for refills on coffee. They want to be within 5 of the true mean when using a confidence interval of 99%. The standard deviation is estimated at 30.
How many customers must they sample?
Customers: ______

A community wants to estimate the proportion of residents who are pet owners. They want to be within 8% of the true proportion when using a confidence interval of 90%.
How many residents must be sampled if no preliminary estimate is available?
Remember when calculation a sample size, we need to round up to the next whole number (not to the closest whole number) if needed.
Residents: _______

https://brainmass.com/statistics/confidence-interval/confidence-interval-sample-size-391456

#### Solution Preview

1. A Company surveys 32 randomly selected employees and ask the number spent working at home after hours during a week. The results as shown below:
10 5 0 8
0 3 4 4
2 3 8 1
4 1 7 5
7 6 2 1
0 5 7 5
10 5 3 6
6 2 2 3

Using Excel, construct a 90% confidence interval for the mean hours worked.
90% confidence interval: __________ +/- ________
90% confidence interval: __4.21875__ +/- _0.811524971__
Since the sample is fairly large, we can use the normal distribution for the construction of CI.
The confidence interval is given by
Confidence Interval Estimate for the Mean

Data
Population Standard Deviation 2.790934345
Sample Mean 4.21875
Sample Size 32
Confidence Level 90%

Intermediate Calculations
Standard Error of the Mean 0.49337215
Z Value -1.644853627
Interval Half Width 0.811524971

Confidence Interval
Interval Lower Limit 3.41
Interval Upper Limit 5.03

Thus with 90% confidence we can claim that the mean hours worked is within (3.41, 5.03) hours.

2. The weights (in ounces) of 12 randomly sampled cakes as shown in the table ...

#### Solution Summary

The solution provides step by step method for the calculation of confidence interval and sample size. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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