Question

Q1 a) What question does a t-test answer?

b) When does a t-distribution begin to look like a normal distribution?

c) What are measures of central tendency?

d) What does the variance measure and how do you calculate it?

Answer 1

Solution:

a) A t- test gives signifiacnce between hypothetical sample mean and population mean. It is also used to check whether there is a significant difference between means of two groups. It tests the means when the observations are paired. It is also used in regression line analysis and partial and multiple correlation coefficient.

b) When the number of degrees of freedom is large then t-distribution converges to normal distribution.t distribution and normal distribution gives approximately same results but when sample size is less than 30 t distribution gives more precise results. However, when sample size is grateer than 30 t distribution converges to normal.  

c) Central tendancy is the centre value of probability distribution.most common measures of Central tendancy are mean ,mode and median. Choosing the best measure of Central tendancy depends upon data.

Mean is the arithmetic averege . The formula for mean is sum of all observations divided by total number of observations.

Median is the value which divides whole data into two equal parts. It is the middle value of data.

Mode is the value which occurs most frequently. It is the most repetitive value in data set.

The other measures of Central tendancies are geometric mean, Harmonic mean, Tream mean,Interqurtile mean, midrange etc.

d) Varaince is the average of squared difference from the mean. Variance measures how far aset of dat is spread out. The process of finding variance is

1) Calculate average of given data set.

2) Substract each value from average to find it's distance from mean.

3) Square all distances.

4) Add all distances.

5) Divide the number obtained by total no of observations. That is,