Expert: Scott A Wilson - 3/17/2009

Question
Dear Sir,

Plz help me in soving following questions......

A small accounting firm pays each of its five clerks Rs 25000, two junior accountants Rs
60000, and the firm’s owner Rs 255000. What is the mean salary paid at this firm? How
many of the employees earn less than the mean? What is the median salary?
2. Nonstandard dice can produce interesting distributions of outcomes. You have two balanced,
six-sided dice. One is a standard dice, with faces having 1,2,3,4,5 and 6 spots. The other die
has three faces with 0 spots and three faces with 6 spots. Find the probability distribution
for the total number of spots Y on the up-faces when you roll these two dice.
3. What is a chi-square test? How do you find the degrees of freedom in a chi-square
distribution? Discuss chi-square test as a test for goodness of fit and as a test of independence.
4. A study of iron deficiency among infants compared samples of infants following different
feeding regimens. One group contained breast-fed infants, while the children in other group
were fed a standard baby formula without any iron supplements. Here are summary results
on blood hemoglobin levels at 12 months of age.
Group n Mean s
Breast-fed 23 13.3 1.7
Formula 19 12.4 1.8
a. Is there significant evidence that the mean hemoglobin level is higher among breastfed
babies? State null hypothesis and alternate hypothesis and conduct a t-test.
b. Give a 95% confidence interval for the mean difference in hemoglobin level between
the two populations of infants.
5. What do you mean by a seasonal index? Explain ratio to link relatives method of measuring
seasonal variations.

Answer
1. A small accounting firm pays each of its five clerks Rs 25000, two junior accountants Rs 60000, and the firm’s owner Rs 255000. What is the mean salary paid at this firm? How many of the employees earn less than the mean? What is the median salary?

To find the average, take (5*25 + 2*60 + 225)1000/(5+2+1).

The number of people making less would be found by computing this value and seeing how many make left.  Just as an approximation, I would expect it to be the five clerks who make less.

I believe the median salary is the 25K that the clerks make.
Since there are 8 people involved, toss out the top 3 and the bottom 3.  Avearge the two that are left.


2. Nonstandard dice can produce interesting distributions of outcomes.  You have two balanced, six-sided dice. One is a standard dice, with faces having 1,2,3,4,5 and 6 spots. The other die has three faces with 0 spots and three faces with 6 spots. Find the probability distribution for the total number of spots Y on the up-faces when you roll these two dice.

The probability would be getting 0 half of the time and 6 half of the time on the second die.  This would give a uniform distribution from 1 to 12 for the outcome.


3. What is a chi-square test? How do you find the degrees of freedom in a chi-square distribution? Discuss chi-square test as a test for goodness of fit and as a test of independence.

Taken from
//www.statisticallysignificantconsulting.com/Chi-Square-Test.htm?gclid=CJTd8MjorJkCFRFWagodaDABJw ,
we have

Chi-Square Example
Suppose we have a hypothesis that the pass/fail rate in a particular mathematics class is different for male and female students. Say we take a random sample of 100 students and measure both gender (male/female) and class status (pass/fail) as categorical variables.
The data for these 100 students can be displayed in a contingency table, also known as a cross-classification table. A chi-square test can be used to test the null hypothesis (i.e., that the pass/fail rate is not different for male and female students).

Chi-Square Statistic
Just as in a t-test, or F-test, there is a particular formula for calculating the chi-square test statistic. This statistic is then compared to a chi-square distribution with known degrees of freedom in order to arrive at the p-value.

We use the p-value to decide whether or not we can reject the null hypothesis. If the p-value is less than "alpha" which is typically set at .05, then we can reject the null hypothesis, and in this case, we say that our data indicates that the likelihood of passing the class is related to the student's gender. See Statistical Data Analysis for more about statistical inference.

The next problem looks like a chi-square.


4. A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, while the children in other group were fed a standard baby formula without any iron supplements. Here are summary results on blood hemoglobin levels at 12 months of age.

Group n Mean s
Breast-fed 23 13.3 1.7
Formula 19 12.4 1.8
It might be better to paste this into a picture and add that as an attachment to the question sicne the columns don't line up at all.
I can see that the first thing in each row is the name of the group.
For the breat-fed, it looks like n=23, mean=13.3, and s=1.7.
For the formula, it looks like n=19, mean=12.4, and s=1.8.

Let the numbers n1, a1, s1 be for group 1.
Let the numbers n2, a2, s2 be for group 2.
The n, a, and s be for number, average, and standard deviation.

a. Is there significant evidence that the mean hemoglobin level is
higher among breastfed babies? State null hypothesis and alternate hypothesis and conduct a t-test.

The null hypothesis is that the means are equal.
The alternative hypothesis would be that they were different.

To compute the statistic, do the following.
t = (a2-a1)/((s2)²/n2 + (s1)²/n1).

b. Give a 95% confidence interval for the mean difference in hemoglobin level between the two populations of infants.

I would look up 95% on the normal table and see what the value was, which I would call N95.

I would then caculate (a2-a1)a1 ± (s1²/n1 + s2²/n2)*N95.


5. What do you mean by a seasonal index? Explain ratio to link relatives method of measuring seasonal variations.

I have never heard of a seasonal index.  I would assume it would be to come up with an equation for the data based on the season of year.