Statistics and Probability Answers

In order to estimate the mean diameter of a variety of orange, a sample of 25 oranges were selected and the sample mean was found to be 7.5 cm with a sample standard deviation of 1.5 cm.

16. The point estimate of the population mean is

Life expectancy Religion A Religion B Religion C No Religion
> 90 years old 27 26 18 29
Take α= 0.05.
H0 : PA = PB = PC = PNO RELIGION = .25
H1 : PA ≠ PB ≠ PC ≠ PNO RELIGION ≠ .25
a. What is the critical value of the chi-square?
b. What is the degree of freedom?
c. What is the value of the test statistics of the chi-square?
d. What is the p-value?
e. Can we conclude that the life expectancy of the Malaysian men depends on their religious affiliation? State your reason.

Year Return
1985 -5.03
1986 49.88
1987 38.73
1988 -14.19
1989 30.4
1990 -19.86
1991 4.37
1992 -19.41
1993 93.36
1994 -5.42
1995 -4.48
1996 -0.75
1997 -38.92
1998 -3.91
1999 28.82
2000 -7.34
2001 18.33
2002 33.35
2003 59.45
2004 8.09
2005 43.79
2006 34.3
2007 36.13
2008 -56.02
2009 76.46
Using data from the past 25 years, an investor wants to test whether the average return of Vanguard’s Precious Metals and Mining Fund is greater than 12%. Assume returns are normally distributed with a population standard deviation of 30%.
a. State the null and the alternative hypotheses for the test.
b. Calculate the value of the test statistic and the p-value.
c. At

Life expectancy Religion A Religion B Religion C No Religion
> 90 years old 27 26 18 29
Take α= 0.05.
H0 : PA = PB = PC = PNO RELIGION = .25
H1 : PA ≠ PB ≠ PC ≠ PNO RELIGION ≠ .25
a. What is the critical value of the chi-square?
b. What is the degree of freedom?
c. What is the value of the test statistics of the chi-square?
d. What is the p-value?
e. Can we conclude that the life expectancy of the Malaysian men depends on their religious affiliation? State your reason.

The probability that Martha will play soccer is 0.3, the probability that Ayyantu will play soccer is 0.4, and they make their decisions independently.

6. The probability that both of them will play soccer is

7. The probability that Martha or Ayyantu or both will play soccer is

8. The probability that both Martha and Ayyantu will not play soccer is

by using statstics, how it could be used by a business to determine if the light bulbs it produces last longer than the competitor’s brand

For the scenarios below, answer the following:
Is the situation Binomial or Hypergeometric?
Referring to your criteria, how do you know which it is?
Change the situation so that it could be calculated using the other distribution.

Scenario 2:
You draw 5 cards from a standard deck of 52 cards. If X is a random variable that represents the number of hearts you get, what is the probability of 3 or more hearts?

Scenario 3:
Your manager at work is giving away tickets for the local Lacrosse game. She has 10 tickets: 4 in the blue section and 6 in the Green section. She gives you two at random. What is the probability that they are both in the blue section?

Scenario 4:
40% of the music you listen to is by a Canadian artist. If you listen to 10 songs, what is the probability that 5 of them are by Canadian artists?

given a family with two children, find the prabability that both are boys, given that at least one is a boy.

A District Commissioner (DC) is worried about the rising numbers in high blood
pressure related deaths in her district, and she wants to end the problem. A
reputable research officer has claimed that the situation is probably as a result of
the ageing population of the district. Ten hospital patients were sampled from the
district, and their blood pressure (Y) and age (X) were summarized as follows:
Patient 1 2 3 4 5 6 7 8 9 10
Age 20 25 50 30 45 60 10 15 35 70
Blood
pressure
80 85 125 90 100 135 80 70 100 140