Statistics: CI, Sample Size, Normal Probability & Regression

1.A random sample of 48 days taken at a large hospital shows that an average of 38 patients was treated in the emergency room per day.
The standard deviation of the population is 4.

Find the 99% confidence interval of the mean number of ER patients treated each day at the hospital.

2.Using the same information as in question 1 above, if the director wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability, what size sample should she choose?

3.The amount of soft drink filled by a machine at a bottling company is supposed to have an average of 12 fluid ounces and a standard deviation of 0.5 fluid ounces if the machine is calibrated accurately. The quality control manager has collected data on 250 bottles of soda that have come off a production line on a randomly selected day. He wants to find out if the amount of soft drink filled can be represented by a normal distribution with the average of 12 fluid ounces and the standard deviation of 0.5 fluid ounces.

The results are as follow:

AMOUNT FREQUENCY

10.5 - under 11.0 4
11.0 - under 11.5 35
11.5 - under 12.0 87
12.0 - under 12.5 93
12.5 - under 13.0 28
13.0 - under 13.5 3

Referring to the table above, what is the expected frequency for the amount of soft drink filled between 11.5 and under 12.0 fluid ounces?
What is the value of the chi-square test statistic?
What are the degrees of freedom?
What's your conclusion at a 5% level of significance?

4.A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices.
Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:

City Price ($) Sales
River Falls 1.30 100
Hudson 1.60 90
Ellisworth 1.80 90
Prescott 2.00 40
Rock Elm 2.40 38
Stillwater 2.90 32

Using the table above solve for the following questions:

What is the estimated average change in the sales of the candy bar if price goes up $1.00?
What percent of the total variation in candy bar sales is explained by prices?

5.The linear trend forecasting equation for an annual time series containing 40 observations (from 1963 to 2002) on real net sales (in billions of constant 1995 dollars) is:

Ŷi = 1.2 + 0.5Xi

What is the fitted trend value for this time series on real net sales for the tenth year?