Question

Think of a problem/issue in your job or in life that can be addressed using a hypothesis test. Present your problem using the null and alternative hypothesis test setup. Also, be sure to present the Type I error as it applied to your problem.  

Answer 1

In a job of data entry, the problem is that I put some of the entries as wrong. The company will cut my salary by 1000 rupees if I make more than 10 entries as wrong on an average a day.

The company wants to know whether I'm running according their conditions or not, hence they will take a sample of 10 days and will find out number of wrong data entries each day and will note down.

Suppose this numbers follow normal distribution given as,

7, 8, 4, 11, 12, 5, 6, 8, 10, 9

Then company will test the hypothesis :

Null hypthesis

H0 : wrong entries are 10 on an average a day

= 10

V/s

Alternative hypothesis

H1 : wrong entries are more than 10 on an average a day

> 10

(the company will take equal type H0 as if it finds out H0 is true then their condition is satisfied,but if H0 gets rejected then they will cut my salary and hence they won't care about average of less than 10)

The test statistics under H0 will follow tn-1,

As standard deviation is unknown.

Same means = xbar

Standard deviation = s

n : number of observations in sample

Population Mean under H0 =0

Test statistic under H0 :

( Xbar - 0) / (s/n)

Type I error will be probability of concluding that my average wrong entries are more than 10 even if they are 10 (under H0)