Statistics and Probability Answers

ACTIVITY 5.2 MEASURES OF CENTRAL TENDENCY

Calculate the Mean, Median and Mode of the following survey data. Show your solution. Follow the steps in the handouts.

1. A gardener buys 10 packets of seeds from two different companies. Each pack contains 20 seeds and he records the number of plants which grow from each pack.

COMPANY A: 20, 5, 20, 20, 20, 6, 20, 20 , 20, 8
COMPANY B: 17, 18, 15, 16, 18, 18, 17, 15, 17, 18

a. Find the mean, median, and mode for each company’s seeds.
b. Which company does the mode suggests is best?
c. Which company does the mean suggests is best?
d. Which company does the median suggests is best?

(answer and draw it into table.thankyou)

A sample of 100 has a mean of 15. Assume that the population is approximately normally distributed a population standard deviation of 4. The hypothesis desired are: Ho; µ = 12.5, Ha; µ ≠ 12.5. Test the hypothesis at a level of significance of 0.02.

A simple random sample of size n drivers were asked if they drive a car manufactured in a certain country. Of the drivers​ surveyed, responded that they did. Determine if more than half of all drivers drive a car made in this country at the level of significance. Complete parts ​(a) through ​(c).
​(a) Determine the null and alternative hypotheses.
​:
p
equals

​:
p
greater than
​(b) State the conclusion for the test.
Choose the correct answer below.
A.
because the​ P-value is the level of significance.
B.
because the​ P-value is the level of significance.
C.
because the​ P-value is the level of significance.
D.
because the​ P-value is the level of significance.
​(c) State the conclusion in context of the problem.

3. Bag A contains 30 balls of which 9 are yellow and 6 are green. Bag B contains 34 balls of
which 14 are yellow and 11 are green. A ball is drawn at random from each bag. (a) Draw a
Probability Tree Diagram to show all the outcomes the experiment. (b) Find the probability
that: (i) both are yellow. (ii) both are green. (iii) one green and one yellow. (iv) at least one
yellow.

Consider 2 triangular dies (each has 4 faces) one blue and another red.

Let Y be a random variable associated with the result of the blue dice. Let X be a random variable that takes the maximum of the two showing numbers.

1. What is the joint distribution of X and Y (draw a table)

2. Calculate the marginal distributions of X and Y.

3.Are X and Y independent? Justify.

all of the steps on a certain ladder fail 2% of the time. If Maria is going to climb up all 23 steps, what is the probability that none of the steps will fail?

In a shipment of bananas, 10% are rejected because they are too small. What is the probability that in a box of 80 bananas at most 8 will be rejected because they are too small?

A factory manufactures light bulbs for distribution under 2 different brands. Brand A bulbs have an average life of 1800 hours with a standard deviation of 240 hours; Those of mark B have an average life of 1450 hours with a standard deviation of 150 hours. A sample of 250 light bulbs is taken from each brand. Describe completely this situation, define all the data, and explain the method and all steps of computation. How likely is the average lifespan of Brand A bulbs to be at least 400 hours longer than that of Brand B bulbs?

1. Currently, total average time a patient spent time in a local health clinic is 47 minutes. A new procedure which is computer based system is being introduced by the management. Based on sample of 12 patient, the new mean spent time is 39 minutes with standard deviation of 6.9 minutes. Test whether the new system is better than the old system using 5% significance level.
2 Following a recent severe typhoon hit the National University of Malaysia, many buildings including lecture halls were badly affected. The management team must decide whether the campus is still safe for conducting a lecture or otherwise. If the null hypothesis is "safe to conduct lecture" and the alternative hypothesis is "not safe to conduct lecture", which error (type I error or type II error) is more important to avoid? Explain your answer

a. Find the p-value of the following test given that
x = 990, n = 100, and σ = 25.
H0: μ = 1000
H1: μ < 1000
b. Repeat part (a) with σ = 50.
c. Repeat part (a) with σ = 100.
d. Describe what happens to the value of the test statistic
and its p-value when the standard deviation
increases.