Question

1. For a company whose total number of employees is 100, we collect data from 7 employees ,5.2, 4.1, 10, 6.8, 3.8, 8.0, and 8.3.

Using these data, write down the upper bound of the 99% CI for population mean. Assume that these data are from a normal distribution.

Please provide answer with 2 decimal points.

2. From a sample of size 250, number of females is 173. What is the point estimate of population proportion?

Provide an answer with 3 decimal points.

3. Which one is the point estimate of population mean?

	a.	sample mean
	b.	sample proportion
	c.	sample median
	d.	sample maximum

4. A survey of 1,206 people asked: “What would you do with an unexpected tax refund?” Forty-seven percent responded that they would pay off debts (Vanity Fair, June 2010).

if the population size is 5000, then write down the upper bound of 95% confidence interval of the population proportion.

An article in the National Geographic News (“U.S. Racking Up Huge Sleep Debt,” February 24, 2005) argues that Americans are increasingly skimping on their sleep. A researcher in a small Midwestern town wants to estimate the mean weekday sleep time of its adult residents. He takes a random sample of 80 adult residents and records their weekday mean sleep time as 6.4 hours. Assume that the population standard deviation is fairly stable at 1.8 hours.

Write down the upper bound of 95% confidence interval.

Answer 1

1. For the given sample mean and standard deviation is as below:

Create the following table.

data	data-mean	(data - mean)2
5.2	-1.4	1.96
4.1	-2.5	6.25
10	3.4	11.56
6.8	0.2	0.04
3.8	-2.8	7.84
8.0	1.4	1.96
8.3	1.7	2.89

Find the sum of numbers in the last column to get.

So standard deviation is

t value for 6 df is TINV(0.01,6)=3.707

So Margin of Error is

Hence CI is

Hence the upper bound of the 99% CI for population mean is 9.86