Quiz 1 | MATH 4993

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Q1: A recent article in the British journal Lancet reports that babies who were fed mother’s
milk tended to have a higher IQ than formula-fed babies. Suppose that two groups of babies
are compared, a group fed mother’s milk and a group fed formula. The resulting IQ scores are
as follows:
Mother 121 105 111 119 108 101 90 131
Formula 101 110 107 98 89 86 117 113 87

(a) Assume that the IQ scores are normally distributed with mean and variance
2 for
mother-fed babies, and with mean and variance
2 for formula-fed babies.

Justify the above underlined statement.
Write down your detailed procedure how to justify the statement first, and then state
the null and alternative hypotheses clearly, your p-value, and then draw all of your
conclusions specifically at 0.1 level of significance with evidence.

(b) Test the normality assumptions for each of the above two groups of babies by using
 Shapiro-Wilk test (if the last digit of your student ID number is an odd number)
 Cramer-Von Mises (if the last digit of your student ID number is an even number)
Draw your conclusions specifically at 0.03 level of significance with evidence.

Q2: The following data are the number of crimes reported to a certain polica station for each
day of a one-week period. Test if the crime is uniformly distributed across days of the week at
a significant level of 0.1.
Day Sun Mon Tue Wed Thu Fri Sat Total
# of crimes 48 38 31 40 39 40 44 280
(a) What are the null and alternative hypotheses?
(b) Write down your p-value, and draw your conclusion specifically with evidence.


Quiz 1 | MATH 4993

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Q3: Fill in the following table and test if the data shown in the table are from a Poisson
distribution.
Value 0 1 2 3 4
Observed
frequency
26 32 24 14 4
Expected
frequency
(make your value)




Please show all of your working steps how to find the expected frequencies (correct to 2 decimal
places), and then write down your p-value and draw a conclusion specifically with evidence.


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