M2A1 Fast Technologies
Connie Smith has sent you a new Excel data file Fast_Technologies_Data_M2A1 and asks that you analyze it.
- The worksheet, Disc Response, contains the recorded response times in microseconds of 400 2TB SSDs selected at random from the production line.
- Do the data in the worksheet appear to be normally distributed? Find and report the minimum value, max value, the range, mean, and standard deviation. Construct a frequency distribution and histogram (use 14 bins and round your bin width up to the nearest tenth of a microsecond) and use them to draw a conclusion. Remember neither a bar or column chart are true histograms which do not have spaces between the columns/bars.
- If the distribution is not normal, what distribution might better represent the data?
- Could any of the response times be considered outliers?
- Using these values for the mean and standard deviation, and assuming the population from which the data are are drawn is normally distributed:
- Find the probability that the response time will exceed 5.20. What is the probability the response time will be less than 4.80?
- What is the actual percentage of response times that are greater than 5.20 or are less than 4.80?
- How do the normal probability calculations compare to the actual occurances? What do you conclude?
- Using the data in the tab 1 TB SSD Test for Model x:
- What fraction of SSDs fails for each of the 30 samples? What distribution might be appropriate to model the failure of an individual SSD?
- Using the data, estimate the sampling distribution of the mean, the overall fraction of failures, and the standard error of the mean?
- Is a normal distribution an appropriate assumption for the sampling distribution of the mean? Why or why not?
- Using all the data, what fraction of SSDs fails the test? Using this result, what the probability of having x failures in the next 100 SSDs tested, for x = 0 to x = 20?
- Fast conducted a survey of SSD brand preference of 300 potential customers and the results are shown in the Brand-Gender
- Construct a cross-tabulation (also known as a contingency table) of the data summarizing the counts for each brand for each gender.
- Complete the contingency table to include all marginal probabilities.
- Find the conditional probabilities of each brand given gender. Complete the following table of probabilities. Put the probabilities expressed as a decimal with three significant digits in the blank column on the right.
Probabilities | |
P(Female) | |
P(Male) | |
P(Fast) | |
P(Carbon) | |
P(Sonic) | |
P(Female and Carbon) | |
P(Female and Fast) | |
P(Female and Sonic) | |
P(Male and Carbon) | |
P(Male and Fast) | |
P(Male and Sonic) | |
P(Female or Carbon) | |
P(Female or Fast) | |
P(Female or Sonic) | |
P(Male or Carbon) | |
P(Male or Fast) | |
P(Male aor Sonic) |
- Are the “events” gender and brand independent? Why or why not?
- Submit a succinct report with appropriate tables and graphs linked to your Excel file.
M2A2 Fast Customer Survey Analysis
The more recent data from Fast’s monthly customer survey is now available. The data are the responses on a scale of 1 to 5 on the dimensions of quality, ease of use, price and service. For purposes of this analysis, assume the data are interval.
Using point and interval estimates, as well as other data analysis such as descriptive statistics, to analyze the data. Prepare a 4 to 5-page report to Ms. Smith including appropriate tables and graphs that communicates the important findings of your analysis. Specifically, you should address differences between regions, i.e. are any shown to be statistically significant. This should include both the mean/median scores on each dimension as well as a focus on the top-of-the-box (4 and 5) scores.
Notes:
- One way to present the results of your analysis would be a chart showing the point estimates and confidence intervals for each region for each dimension.
- If the above graph indicates the overlap in confidence intervals is small (if any), e.g. USA and ME above, a table similar to this would be good to include:
Customer Survey Factors | ||||||||||
Pairs | Speed | Reliability | Price | Service | ||||||
USA:AM | Different | Same | Different | Same | =IF(I5>H$4,”Same”, “Different”) | |||||
USA: EU | Different | Same | Same | Same | ||||||
USA:AS | Same | Same | Same | Same | ||||||
USA:ME | Different | Same | Different | Different | ||||||
AM:EU | Same | Same | Same | Same | =IF(I6>H$5,”Same”,”Different”) | |||||
AM:AS | Same | Same | Same | Same | ||||||
AM:ME | Different | Same | Different | Different | ||||||
EU:AS | Same | Same | Same | Same | =IF(I7>H$6,”Same”,”Different”) | |||||
EU:ME | Same | Same | Different | Different | ||||||
AS:ME | Same | Same | Different | Different | =IF(I8>H$7,”Same”,”Different”) |
Solution
AM
AS
EU
ME
USA
Disc response
1 tb ssd
Gender