Business Statistics for Decision Making
Q1. A health scientist
has created three different diet plans for a weight loss program. He conducted
an experiment with 24 volunteers to see the impact on weight loss. He measured
the weights of the volunteers before the start of the diet plan. Then they were
assigned to one specific diet plan for a month. After one month their weights
were measured again. The differences in weights are given in the table below
for each of the diet plans. At the end of the experiment, the scientist wanted
to understand if there is a significant difference in weight loss among the
volunteers of the three diet plans. Read the data table below and answer the
questions.
a. Conduct ANOVA on
the above table. Do you find a significant difference in weight loss due to the
three diet plans? Explain and interpret using both the p-value and F critical
value from the output. Use MS-Excel for the analysis.
·
Why do you think ANOVA
is required to answer this question?
·
What is the formula to
calculate F-ratio? (Only write the formula. You do not need to show the
calculations for F-ratio). (10 Marks)
Q2. Consider the
following sample. It contains the weights of 25 participants:
55, 57, 58, 43, 62,
67, 71, 69, 66, 51, 72, 62.5, 58.5, 61, 72.5, 75, 44, 48, 49, 49.5, 49,
62, 66, 71, 58.
Calculate and plot the following using MS-Excel. Write the formula and show the
steps.
·
Variance
·
Standard deviation
·
Histogram
·
Ogive
Note: For histogram
and ogive use bins numbers as 40, 45, 50, 55, 60, 65, 70 (10 Marks)
Q3. You have been
hired as a researcher for a prominent research-based organization and you have
been allocated a new project for helping out a client. You know that the time
taken to complete similar projects is normally distributed with a mean of 50 days
and a standard deviation of 4 days.
·
What is the
probability of finishing this project within 45 – 55 days? (5 Marks) –
·
When do we use Poisson
distribution? Give two example scenarios. (5 Marks) –
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