Statistics and Probability Answers

Among 157 African-American men, the mean systolic blood pressure was 146 mm

Hg with a standard deviation of 27. We wish to know if on the basis of these data,

we may conclude that the mean systolic blood pressure for a population of African-

American is greater than 140.

• Setup the null and alternate hypothesis (1 mark)

• Determine the type of the test (1 mark)

• Use α=0.01, conduct the test and accept or reject the hypothesis on the basis of

the test. (Given Z_0.99=2.33) (3 marks)

The average number of homes sold by a realty company is 2 homes per day. What is the probability that exactly 3 homes will be sold in the next Sunday.( Given that e=2718)

Suppose there are three different types of cakes that are sold at Tina’s Bakery. There are 4 cheesecakes, 5 vanilla sponge cakes and 2 black forest cakes. Tom takes at random 2 of these cakes without replacement. What is the probability that he takes 2 different types of cakes upon his selection?

The claim is made that Internet shoppers spend on the average $335 per year. It is desired to test that this figure is not correct at a = 0.075. Three hundred Internet shoppers are surveyed and it is found that the sample mean = $354 and the standard deviation = $125. Find the value of the test statistic and give your conclusion. Note: critical value is +1.7805 and -1.7805.

A population consists of the numbers 5, 20, 9, 4, and 2 with sample size of 3

1. Find the t-value that the area in the right tail is 0.10 with 25 degrees of freedom.

2. Find the t-value that the area in the right tail is 0.05 with 30 degrees of freedom.

3. What is the area of the region to the left of t=1.055 with n=30?

4. What is the area of the region to the right of t = 0.687 with df =20?

The average zone of inhibition (in mm) for mouthwash H as tested by medical technology

students have been known to be 9mm. A random sample of 10 mouthwash H was tested

and the test yielded an average zone of inhibition of 7.5 mm with a variance of 25mm. Is

there enough reason to believe that the antibacterial property of the mouthwash has

decreased? Test the hypothesis that the average zone of inhibition of the mouthwash is

no less than 9mm using 0.05 level of significance.

A family has four children find the probability that the family has equal number of sons and daughter.

It is claimed that last year, 65% of the people believed that there was an improvement in the country’s economy.

Suppose this year, only 270 out of the 450 people randomly selected believe that there is an improvement in the country’s

economy. Does this indicate that there is a decrease in the number of people who believes that there is an improvement in

the country’s economy? Use 0.05 significance level.

(Use critical value method)

A History teacher claims that the average height of Filipino males is 163 centimeters. A student taking up Statistics

randomly selects 20 Filipino males and measures their heights. Their heights in cm are shown below.

163 164 165 177

167 163 159 169

159 160 163 163

165 169 163 165

162 174 163 167

Do the collected data present sufficient evidence to indicate that the average heights of Filipino male is different

from 163 cm? Use 0.05 level of significance and assume that the population follows a normal distribution.

(Use critical value method)