Statistics and Probability Answers

No.3. A researcher conducted an experiment on rats and found the below given data of initial weights X of 15 four weeks-old rats and their weight gains Y, after 9 weeks on a special diet. (2+2+1)

Initial weight(X) 55,68,72,43,56,54,62,59,74,73,64,51,70,49,63
Weight gain(Y) 112,95,120,121,122,105,85,89,98,95,104,135,125,118,90

The researcher wish to know
(a) Whether or not the weight gain depends upon birth weight
(b) Is there any relationship between birth weight and weight gain after 9 weeks of special diet.
(c) Interpret your finding in part (a) and part(b). write down the relationship between correlation and regression coefficients.

In a cumulative relative frequency distribution , the last class have a cumulative relative frequency equal to....?

A frequency distribution is a tabular summary of data showing the .....?

Statistics Expressing the Perception of Pastors on Mission
Strongly Agree = 1, Agree = 2, Neutral = 3, Disagree = 4, Strongly Disagree = 5
Item/Statement Mean
Mode Median Standard Deviation
(SD)
1. Every RPAG single member has the responsibility of fulfilling the Great Commission and must participate in funding this effort aside of paying regular tithes and offerings. 1.31 1 1 0.54
2. Jesus called RPAG churches to take the Good News to the whole world. 1.39 1 1 0.67
6. As a pastor, one of my great responsibilities is to prepare my church for the work of mission in foreign lands. 1.53 1 1 0.81
Cluster Mean, and SD
1.41 0.67
Interpret the mean and standard deviation

The number of steps to cover the same distance was measured for 20 randomly chosen people. The sample mean is 2770 steps and the sample standard deviation is 554 steps. Assume distribution to be normal.

Round your answers to the nearest integer (e.g. 9876).


a) Construct a 95% two-sided confidence interval on the mean.
b) Construct a 95% lower confidence bound on the mean.
c) Construct a 95% upper confidence bound on the mean.

2. The number of steps to cover the same distance was measured for 20 randomly chosen people. The sample mean is 2770 steps and the sample standard deviation is steps. Assume distribution to be normal.

Round your answers to the nearest integer (e.g. 9876).


a) Construct a 95% two-sided confidence interval on the mean.
b) Construct a 95% lower confidence bound on the mean.
c) Construct a 95% upper confidence bound on the mean.

1. Dairy cows at large commercial farms often receive injections of bST (Bovine Somatotropin), a hormone used to spur milk production. Bauman et al. (Journal of Dairy Science, 1989) reported that 12 cows given bST produced an average of 28.0 kg/d of milk. Assume that the standard deviation of milk production is 2.25 kg/d.

(a) Find a 99% confidence interval for the true mean milk production.

Round your answers to two decimal places (e.g. 98.76).


_________ < = mu < = ______

(b) If the farms want the confidence interval to be no wider than ±1.25 kg/d, what level of confidence would they need to use?

Express your answer in percent.
Round your answer to the nearest integer (e.g. 98).

confidence = ____%

1. A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. How is the standard deviation of the sample mean changed when the sample size is increased from n=4 to n=52? Round all intermediate calculations to four decimal places (e.g. 12.3456) and round the final answer to three decimal places (e.g. 98.768).

The standard deviation is ( reduced, increased ) by _____ psi.

2. Suppose that X has a discrete uniform distribution

f(x) = {1/3, x=1,2,3
{ 0, otherwise
A random sample of n= 38 is selected from this population. Find the probability that the sample mean is greater than 2.1 but less than 2.4. Express the final answer to four decimal places (e.g. 0.9876).

The probability is _______

6. Define or state the expected value of a discrete random variable X (E(x) is given as____).

Rene is a soccer player who takes 8 independent free shots per game, with a probability of 0.7 of getting a medal on each successful shot, what is the expected number of medals that she gets?