Statistics and Probability Answers

Describe which measure of central tendency-mean, median, or mode was probably used in each situation.

a. One half of the factory workers make more than $5.37per hour and one half make less than $5.37.

b. The average number of children per family in the Plaza Heights Complex is 1.8

c. Most people prefer red convertibles over other colors.

3.3.14 Let X and Y be independent, with X ∼ Bernoulli(1/2) and Y ∼ N(0, 1). Let
Z = X +Y and W = X −Y. Compute Var(Z), Var(W), Cov(Z, W), and Corr(Z, W)

There are 4 red pens, 3 blue pens, 2 black pen, and 4 green pens in a desk drawer. You randomly choose one. Find each probability as a FRACTION in SIMPLEST FORM.

1) If P(z>k) = 0.9554 then k= ?
2) The mean and standard deviation of the age of bank customers with large checking accounts are 44 and 6, respectively. Then the proportion of such customers that have ages between 35 and 53 is?
3) A Highway Patrol reports the mean speed of those traveling along certen highway is 102 kms per hour with the standard is 7.5 kms per hour. Assume the distribution of speeds follows a normal distribution. 91% of car traveling less than what speed?

Two judges at a fete placed the ten entries for best fruit cakes competition in order as follows. What’s the relationship between them?
Entry A B C D E F G H I J
Judge 1 2 9 1 3 10 4 6 8 5 7
Judge 2 6 9 2 1 8 4 3 10 7 5

The accompanying table shows a portion of the number of cases of crime related to gambling (Gambling) and offenses against the family and children (Family Abuse) for the 50 states in the United States during 2010.

a) Determine the 5 summary values and construct a boxplot for gambling. Use it to identify outliers, if any.

Given that a customer owed $1000 or more, what is the probability that the customer received a cash advance? (2 Marks)
Are the events “receiving a cash advance” and “owning $1000 or more” mutually exclusive? Explain using probabilities. (2 Marks)
Are the events “receiving a cash advance” and “owning $1000 or more” independent? Explain using probabilities.

Ecobank Ghana issues its own credit card. The credit manager, Giovina wants to find whether the mean monthly unpaid balance is not at most Ghc400. The level of significance is set at 0.05. A random check of 25 unpaid balances revealed that the average is GHc410 with the standard deviation of GHc20. Should the credit manager conclude that the population mean is not at most GHc400, or is it reasonable that the difference is due to chance?
a. Explain why t is the test statistic to be used here.
b. What is the critical value of the test statistic?
c. What is your decision regarding the H0?
d. Estimate the p-value and use it to decide.
e. Should the credit manager conclude that the population mean is not at most GHc400, or is it reasonable that the difference is due to chance? Explain briefly.

Question 2
A group of reputable housing firms in Ghana claim that the mean price of
residential homes before the change of government does not exceeds the
mean price after the new government in Ghana came to power. Tonaton.com
in Ghana wishing to determine the authenticity of the claim, selected sample of
residential properties to appraise their prices before and after the change of
government. The results, reported in GHc000, are:
Before After
128 135

105 110
119 131
140 142
98 105
123 130
127 131
115 110
122 125
145 149
At the 0.01 significance level:
a) Make your decision using the critical value approach.
b) What is the p-value? Decide with it
c) Mention one assumption that needs to be made about the
distribution of the differences?
d) Is the change of government associated with the higher prices
of residential homes? Justify practically.