10-11 Z test of One Sample Mean and T test Sifnificance

     Today is Tuesday, May 10.2011. A day for Z-test and T-test. Our reporter for this morning ladies and gentlemen is no other than the early girl is Miss Mary Laride.

She discuss first the Z test

     The Z test is a statistical test for the mean of a population. It can be used when n  > 03, or when the population is normally distributed and        is known.

     The formula for the z test is,

      Z =       x - µ              where:

                 /     / n                       X= sample mean

                                                         µ= hypothesized sample        

                                                             Mean

                                                      = population standard

                                                               Deviation

                                                         n=  sample size

     The reporter tried to gave example in this lesson and interpret the result using the table. Maybe it is good for us if we will provide ourselves a complete table for our own advantage.

Second topic for today is the t- Test

     The t test is a statistical test for the mean of a population and is used when the population is normally or approximately normally distributed, is unknown, and n < 30.

    The formula for the t test is

                  T =   x - µ

                        S/  v  n                 

The degree of freedom are d.f. = n-1

     When testing the hypotheses by using the t test, follow the same procedure as for the z-test.

1. State the hypotheses and identify the claim.
2. Find the critical value (s)
3.  Compute the test value.
4. Make the decision to reject or not reject the null hypothesis.
5. Summarize the result.

Here in this kind of test, I learned to be careful of the formula to be used. Be particular also of the operation/s involved.

      Addition to this, I have to update my knowledge in  manipulating computer.

      Thank for this day, though I learned less its up for me to develop this.

     

     To ma’am Mary, thank you for sharing us your blessings.

Reference:

Statistics for Filipino students by Ma. Carmelita A Batacan et. Al.

“NATURE IS THE GREATEST TEACHER AND I LEARN FROM HER BEST WHEN OTHERS ARE ASLEEP. In the still dark hours before sunrise God tells me of the plans I am to fulfill.” George Washington

Statistics In Life

May 16, 2011, Monday.

This research is taken from 2001 Health and Home. Research confirms that stress is more deadly for men than for women.

• Two times as many men die from combined heart disease problems than do women.
• Pneumonia and influenza cause about three times as many male deaths as female.
• Accidents and adverse drug effects kill three times more males the females.
• The ratio of male to female suicides is three males than females.
• Thirty percent more males die form cancer than females (cancer can be stressed related)
• Men live shorter than women by eight years.
• Men exhibit more stress related health problems such as hypertension, arteriosclerosis, heart attack, and their heart failure.

Stress is a result of anything that annoys, threatens. Excites, worries, angers, frustrates, or challenging self-esteem.

“ If you don’t like something, change it. If you can’t change it, change your attitude. Don’t complain.”- Maya Angelou

Statistics In Life

LIFESAVING TIPS FOR A HEALTHY FUTRE:

( By Sandra Gordon)

2004- Health and Home

    The more doctors learn about longevity. They more appreciate the role lifestyle plays in determining health. Research indicates that as much as 70 percent of longevity may be attributed to lifestyle factors-not genes.

     What can you do to improve your odds? Here’s what a number of medical experts say on the subject:

Beat Heart Disease

1. Get your cholesterol tested if you haven’t in the past five years. Ideally your total cholesterol level should be less than 200 mg/dl.
2. If your cholesterol is more than 200, set you mind in checking your lifestyle changes to make it down.
3. Limit fat to no more than 300 percent of calories.
4. Get you blood pressure checked every two years if yours is normal. If it’s high, have it checked yearly.
5. If you have high cholesterol and want to go on or stay on the pill, ask your doctor about formulations that can lower the LDL and raise the HDL.
6. Post a chart or make a graph.

Fight cancer

7. If you smoke, quit.
8. To checked for cervical cancer, women who are sexually active or over 18 should have yearly Pap test.
9. Women should get clinical breast exams every year between the ages 20 and 39, and yearly if they are 40 or older.
10. The Acs suggest that women perform breast self-examinations monthly starting 20s.
11. If you are 40 or older have a yearly mammogram.
12. If you suspect you’re at high risk for breast cancer, talk to your doctor about tamoxifen.
13. at menopause, women at high risk for uterine cancer should have a sample of endometrial tissue examined for dysplasia.
14. To screen for colon and rectal cancer, the ACS recommends that men and women ages 50 and older either a fecal occult blood test yearly.
15. Men ages 50 and older should undergo a prostate-specific antigen blood test and a digital rectal examination to screen for prostate cancer.
16. To get sense of your cancer risk find out types of cancer that occurred in you family and bring this to the attention of the physician.
17. Learn the health threats your job may pose, such as exposure to carcinogenic materials like asbestos.

Did you know that…

• African-American men have the highest incidence of prostate cancer in the world, while the Asian men have the lowest risk?
• For African-American men , the higher of prostate cancer could be attributed to their dark skin color which does not soak up as much vitamin D from the sun, leading to a deficiency?
• For the Filipino migrants to America, the incidents rates of prostate cancer were noted to be 2.5 times higher than those observed in the Philippines?
• Swedish men have a high rate of death due to prostate cancer because there is virtually no screening in their country?
• In 1960 one in 20 American women had breast cancer. Today the figure has grown to one in eight.
• Breast cancer is the second leading cancer among Filipinos, next to lung cancer.
• At age of 50. a Caucasian woman has 1-in-15 risk of developing breast cancer in the next 20 years of her life, while an African-American woman has a 1-in-20 risk. An Asian/Pacific Island woman has a 1-in-26 risk, and the Hispanic woman a 1-in-27 risk.
• From 1998 health and home:  Louise Braille, at the age of 15, invented the Braille alphabet for the vision impaired?/
•  

STATISTICS IN LIFE

When the Smoke Clears;

     Trashing tobacco out of one’s system improves health. Here’s what happens when the smokers quits after.

• 20 minutes, blood pressure and pulse rate returns to normal.
• 8 hours, oxygen levels in blood return to normal.
• 24 hour, carbon monoxide is eliminated form the body.
• 48 hours nicotine is no longer detectable in the body.
• 72 hour, breathing becomes easier as the bronchial tubes relax.
• 2-21
• Weeks walking becomes easier as circulation improves throughout the body.
• 3-9 months breathing improves as coughing, shortness ob breath and wheezing incidence decline. Lung function increase by 5-10 percent.
• 5 years, risk of heart attack falls to about half that of a smoker.
• 10 years, it’s like you never smoke as risk of heart attack falls for about the same as that of a non-smoker.

     Indeed, the only quitters that win are the smokers.

                                          Health And Home 2004

12. ANALYSIS OF VARIANCE (ANOVA)

     This topic was done by Miss S. Ancino and Miss C. Dalut. May 12-13,2011.

     They started their task after Prof. Robles reviewed the past lessons.

    

     When F-test is used to test a hypothesis concerning the means of three or more populations, the technique is called Analysis Of Variance (ANOVA).

     A marketing analyst wishes to see whether there is a difference in the average time a customer has to wait in the checkout line in three large department stores.

Shoe Mart	Robinson’s	Rustan’s
3	5	1
2	8	3
5	9	4
6	6	2
3	2	7
1	5	3
X=3.33	X=5.83	X=3.33
S12=3.47	S12=6.17	S12=4.27

At a =0.05, is there a significant difference in the mean waiting times of customers for each store?

Solution.

Step1. state the hypothesis and identity the claim.

          H₀: There is no significant difference in the mean     waiting times of customers for each store.

         H₁: At least one mean is different from the others. (claim)

 Step11. Find the critical value. Since k=3, N=18 and a = 0.05.

         dfN= k-1 = 3-1=2

         dfD= N – k= 18-3 =15

          The critical value is 3.68

Step 111. Compute the test statistic.

1. find the grand mean

X_GM = Ʃx   = 3+2+…+3  = 4.17

            N             18

2. Find between group variance

S²_B  =  Ʃn_i ( x_i - x_GM )²

                                      k-1

                         =6(3.33-4.17)²+6(5.83-4.17)²+6(3.33-4.17)²

                                                             

                                                  3-1

                         = 25/2 = 12.5

3. Find the within group variance

S²_w = Ʃ(n₁ – 1)s_t²   

              Ʃ(n_i -1)

      = (6-1)(3.47)+(6-1)(6.17)+(6-1)(4.27)

               (6-1)+(6-1)+(6-1)

      = 96.6/15

      = 4.64

                              

4. Find the F-test value

F=  s²_B / s²_B =     12.5/4.64        =  2.69

Step 4. make a decision. Since 2.69 < 3.69, the decision is not to reject the null hypothesis.

Step 5. Summarize the result. There is not enough evidence to support the claim that there is a difference among the mean waiting times in the three department stores.

ANALYSIS OF VARIANCE TABLE

Source	Sum of squares	df	Mean squares	F
Between	SSB	k-1	MSB	F
Within	SSw	N-k	MSw	F

SS_B  - sum of the squares between

SS_{w –}  sum of the squares within

N= n₁ +n₂ +…+n_{k –} sum of the sample size in the group.

MS_B = SS_B/ k-1

MS_w = SS_w/ N-k

F  = MS_B/MS_w

Source	Sum of Squares	df	Mean Squares	F
Between	25	2	12.5	2.69
Within	69.6	15	4.64
	94.6	17

                              

Reference: statistics for Filipino students by Ma. Carmella A. Batacan

ANOVA will be used as statistical tool for treatment if the data is composed of more than three variables.

According to former Pres. Fedil V. Ramos. “ If one hundred years in the life of the nation is a momentous occasion which compels as to take stocks of ourselves as a people and to take a serious and realistic look at who we really are , where we have come from and where we are going.”