Student’S t Distribution And Its Applications

A test was conducted with $6$ Students before and after the training program. Their marks were recorded and tabulated as shown below. Test whether the training was helpful in improving their scores.

The marks secured by 9 students in Statistics and that of $12$ Students in Business Mathematics are given below:

Test whether the mean marks obtained by the students in Statistics and Business mathematics differ significantly at $1\%$ level of significance.

An IQ test was conducted to $5$ Persons before and after they were trained. The results are given below:

Test whether any change in IQ at $1\%$ level of significance.

The number of pages typed by $5$ DTP-operators for 1 hour in the morning sessions are $10,12, 13, 8, 9$, and the number of pages typed by them in the afternoon are $11, 15, 12, 10, 8$. Is there any significant difference in the mean number of pages typed?

Samples of two types of electric bulbs were tested for life (in hours) and the following data were obtained.

Test the hypothesis that the population means are equal at $5\%$ level of significance.

The heights (in feet) of $6$ rain trees in a town $A$ are $30$, 28, 29, 32, 31, 36 and that of 8 rain trees in another town B are 35, 36, 37, 30, 32, 29, 35, 30. Is there any significant difference in mean heights of rain trees?

The average run of cricket player from the past records is $80$. The recent scores of the player in $6$ test matches are $84$, $82$, $83$, $79$, $83$ and $85$. Test whether the average run is more than $80$

A random sample of $10$ packets containing cashew nuts weigh (in grams) $70$,$120$,$110$,$101$,$88$,$83$,$95$,$98$,$107$,$100$ each. Test whether the population mean weight of $100$ grams?

A random sample of ten students is taken and their marks in a particular subject are recorded. The average mark is $60$ with standard deviation $6.5$. Test the hypothesis that the average mark of students is $55$.

Write down the procedure to test significance for equality of means of two normal populations based on small samples.

Explain the testing procedure to test the normal population mean, when population variance is unknown

Write down the applications of $t$-distribution

List out the properties of $t$-distribution

Write the standard error of the difference between sample means.

Write the test statistic to test the difference between normal population means.

When paired t-test can be applied?

Define the paired t-statistic.

Define: degrees of freedom.

 Define student’s$t$-statistic

If ${s_1}^2$ and ${s_2}^2$ are respectively the variance of two independent random samples of sizes ‘m’ and ‘n’. Then standard deviation of the combined sample is