[answered] 1. In the general population, the height of an individual m

1. In the general population, the height of an individual male is a normally distributed random variable,

with the population mean of 62 inches and the population standard deviation of 10. What is the

probability that the sample mean calculated from a random sample of 25 males will be greater than 60

inches? 2. You are on a remote island studying the rate of incidence of a rare highly contagious infectious disease

Plants. You have a random sample of 20 people from the island. 15 of them developed Plants.

Provide the exact 97.5% two-sided confidence interval for the true rate of incidence of Plants (exact

means DO NOT use the normal approximation to the binomial). (Hint: this problem can be described by

the binomial distribution) 3. Mark which of the following statements are true (T) and which are false (F).

a) You have a normally distributed random variable X ~ N(?=10,?2=25).

For this variable, P(X = 5) = 0

b) You have a normally distributed random variable Y ~ N(?=1,?2=1).

For this variable, P(-1 &lt; Y &lt; 1) ? P(-1 ? Y ? 1)

c) You have a binomial random variable B ~ Binomial(n=100, p=0.6).

For this variable, P(B &gt; 40) = P(B ? 40)

d) You have a normally distributed random variable Z ~ N(?=0,?2=1).

For this variable, P(Z &lt; -1) = P(Z ? 1) 4. Suppose, you wish to compare two weight loss programs, X and Y. In your experiment, you use pairs of

test subjects matched on age, sex, and degree of obesity. One member of each pairs goes through

program X, the other goes through program Y. The results for 100 pairs showed that for 40 pairs both

programs are effective, for 20 pairs both programs are ineffective, for 15 pairs program X is effective

whereas Y is not, for 25 pairs program Y is effective whereas X is not. What contingency table-based test

should we perform to compare these two programs? Provide the following:

a) Present the data in the form of a 2x2 contingency table.

b) State what contingency table-based test you will use and its H0 and H1. c) Perform the test at the significance level of 0.05, find the p-value, and make a final conclusion about

the data. 5. In contingency tables analysis the expected tables is created by:

a. assuming the variables are independent

b. under the assumptions of the null

c. a and b

d. neither 6. The Sign Test is a better test to use than the one-sample t-test because

a. it is more powerful

b. it can be used anytime

c. it is easier to use

d. it gives the same results

e. ... it is not a better test to use ? ever 7. If we have an outlier in our data we should:

a. remove it from the analysis

b. change the value to the mean of the variable so it doesn?t affect the analysis

c. analyze the data with and without the outlier and report the results

e. none of the above

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