Statistics and Probability Answers

1.      Two examples are randomly selected from two groups of students who have been taught using different teaching methods. An examination is given and the results are shown below:

Group 1                               Group 2

N1 = 8                                  n2 = 10

Mean of Grp 1 =85         Mean of Grp 2 =87

Variance of Grp 1 =46    Variance of Grp 2 = 36.

               Using a .05 level of significance, can we conclude that the two different teaching methods are equally effective?

1. Evaluate the mean and standard deviation for the following.

(a) The young modulus^(GN/m^2) for stainless steel is given by:

Young modulus 193 194 195 196 197 198 199 200

Frequency 7 7 10 19 13 9 8 3

B) The tensile strength of the aluminum alloy is given by:

Tensile strength T / frequency

320^ ≤ T < 350 4

350^ ≤ T < 380 12

380^ ≤ T < 410 18

410^ ≤ T < 440 16

440^ ≤ T < 470 15

470^ ≤ T < 500 10

500^ ≤ T < 530 3

530^ ≤ T < 560 7

An urn contains 12 white, 5 yellow and 13 black marbles, a marble is chosen at randok from the urn, and it is noted that its not one of black marbles. What is the sample space in view of this knowledge? Whats the probability thats yellow?

A medical researcher wants to begin a clinical trial that involves systolic blood pressure (SBP) and cadmium (Cd) levels. However, before starting the study, the researcher wants to confirm that higher SPB is associated with lower Cd levels. Below are the SBP and Cd measurements for a sample a participants. What can the researcher conclude with 𝛼 = 0.10?

Cd

55.9

55.7

55.7

55.5

55.9

55.8

55.8

55.5

55.7

55.8

55.6

SBP

169

161

115

113

182

126

179

127

148

160

140

1. Over the past 30 games between team A and team B, team A has won 14 times, team B has won 11 times and the game has ended in a draw 5 times. If these two teams played 9  games this season, what is the probability that team �� would win 5 games, team �� would  win 3 games, and the remaining game would be a draw? 

2. The formula for the standard error (standard deviation of the distribution of sample  means) implies that as the sample size (n) increases, the size of the standard error  decreases. Explain the role of the standard error in comparing the sample mean and the  population mean. Use the definitions and concepts on sample means distribution and  standard error and show examples comparing the sample mean and the population mean  of a distribution when the standard error changes in value to express your answer.

Weights of newborn babies in a particular city are normally distributed with a mean of  3380 g and a standard deviation of 475 g. 

a. A newborn weighing less than 2100 g is considered to be at risk, because the  mortality rate for this group is very low. If a hospital in the city has 500 births in a  year, how many of those babies are in the “at-risk” category?

b. If we redefine a baby to be at risk if his or her birth weight is in the lowest 3%,  find the weight that becomes the cutoff separating at-risk babies from those who  are not at risk. 

c. If 20 newborn babies are randomly selected as a sample in a study, find the  probability that their mean weight is between 3200 g and 3500 g.

1. PICH – A – HOY is one of the best-selling cookie companies in a certain country. Assume that the weights of all packages of these PICHA-HOY cookies are normally distributed with a mean of 35 ounces and a standard deviation of 0.5 ounces. Find the probability that the mean weight, of a random sample of 20 packages of this brand of cookies will be between 34. 3 and 34. 8 ounces. Draw the curve to illustrate the problem.

if population has a variance of 7.4 what is the variance of the sampling distribution of it means?the sampling distribution has a sample size of 2 and all possible samples are drawn with repalacements

The average lifespan of a Ghanaian is 57years. The average lifespan of males in Ghana is known to be 55years while the average lifespan of females in Ghana is known to be 60 years. The average lifespan of people from the Northern region of Ghana is known to be 58 years while the average lifespan of people in the East region of Ghana is known to be 54 years. 

Use the above information to answer the following questions:

(i).With your reasons, discuss all possible population parameters from the above information.

(ii).With your reasons, discuss all possible sample statistics from the above information.

(iii) Compare and contrast the average lifespan of males and females. Which group average is more likely to represent the corresponding population parameter? Give reasons for your answer.