Part 1
1. The following table contains measurements of the inside diameters of machined parts (0.01 mm).
a. Calculate the sample means for each of the 10 samples.
b. Calculate the overall process mean, x-bar.
2. Data-entry clerks at a large insurance company key in thousands of insurance records each day. Samples of work of 20 experienced clerks is shown in the table below. 12 Records entered by each clerk were carefully examined to determine if they contained errors.
Process mean = 0.30 and process std deviation = 0.231. Calculate the 3-SEM upper and lower control limits for an x-bar control chart of data entry.
[You don't need to plot a chart.]
3. A pharmaceutical manufacturer must control the concentration of active ingredient in a chemical process.
The optimum concentration is 10% and the following data is collected in 12 sample sets.
a. Construct/plot an x-bar control chart of the chemical process.
b. Is the process in control? Why or why not?
4. A value, x = 18.8, is sampled from a normal distribution having mean = 32.7 and standard deviation = 6.4.
a. Calculate the Z-score for x = 18.8
b. Explain the meaning of the Z-score value you calculated.
5. An online advertiser measures the "stickiness" of its ads by the browse duration of a webpage. Browsing data is sampled throughout the advertisement's run as a check of the host's system reliability. The following data is a small subset of such a sampling of ad duration (in seconds).
a. Calculate the sample mean and sample standard deviation of the 300 observations.
b. Assign a Z-score to each sample observation.
c. The advertiser classifies any duration greater than 3s distant as an outlier. Identify all 3s outliers in the data.
Part 2
1. A company has profit ($000) and revenue ($000) over the past 9 periods.
a. Calculate the Spearman rank correlation coefficient between revenue and profit
b. Calculate the Pearson product moment correlation coefficient for revenue and profit
c. Comment on the association between revenue and profit.
2. A study was conducted to determine the relationship between travel miles and charges on the American Express card. A research firm selected a random sample of 25 cardholders and recorded total miles traveled and total credit charges over a specified period.
a. Construct a scatterplot of miles (x) versus dollars (y)
b. Determine the linear regression equation for travel expense dollars based on miles driven. Be sure to write your answer in equation form.
c. Plot the regression line on your scatterplot
3. You are a naturalist capturing wild black bears to measure their approximate age (in months) and weight (in kilograms).
a. Determine the linear regression equation for age (x) and weight (y).
b. Calculate the coefficient of determination, r2.
c. You are preparing a symposiom presentation of your findings and wish to make a key point of the coefficient of determination. How would you interpret or explain your calculated r2 value?
4. A health insurer estimates the cost of treatment (y) based on the average number of hospitalization days recommended by the examining physician (x).
y = 453.96 + 11207.28x
a. If an examining physician recommends a hospital stay of 6 days, what is the estimated treatment cost?
b. What is the expected increase in treatment cost for every additional day of hospitalization?
5. Assume inventory is growing by day. Make a scatterplot of the data and use "Add Trendline" to fit 2 non-linear trends: Power and Polynomial (order=3). Which one fits the data best and why?
Attachment:- Assignment.rar