1 an organization wants to apply cost cutting measures for...

An organization wants to apply cost-cutting measures for improving efficiency. As the first step, they want to reduce telephone expenses incurred by employees. For this, the organization takes a random sample of 10 employees to gather the following data (in thousands rupees) in previous years: 10, 12, 24, 23, 11, 14, 15, 34, 16, 23. Construct a 95% confidence interval to estimate the average telephone expenses of the employees in the population. Write all the assumptions selecting the sampling distribution.

Transcript

00:01 So an organization wants to apply cost -cutting measures for improving efficiency.

00:04 As the first step, they want to reduce telephone expenses incurred by employees.

00:08 For this organization to take a random.

00:10 For this, the organization takes a random sample of 10 employees to gather the following data.

00:16 So we are supposed to construct a 95 % confident interval to estimate the average telephone expenses of the employees in the population.

00:23 So we have our sample size to be 10 and to construct a 95 % confidence interval for the population, mean of the expenses of employees regarding the telephone expenses we are going to be using format that says m is equals to x but we have plus or minus we have a critical value times s divided by the square root of n so we need to get the value of the sample mean which is x bar the value of the sample standard division which is s and the critical value so to get the sample mean and the samples that are division we need to use our descriptive statistics so we make use of the calculator to get the value of the sample mean and the sample standard deviation so this my calculator these are data already pasted in here so we press calculate as you can see our sample mean is 18 .2 so that means x bar is equals to 18 .2 and our s which is the sample standard deviation is going to be having a value of 7 .59 let's approximately say 7 .60 to 2 decimal place so that 7 .60 so the next thing is for us to get our critical value and to get our critical value we need the degree of freedom and degree of freedom is usually the sample size minus one so in this case that is 10 minus 1 which gives us 11 our confidence level here is 95 percent which simply implies that our alpha level is actually 5 percent so the next step is for us to move into our calculator so uh to get our critical value so our test is two -tailed our critical value our degree of freedom's radar is 9 and our level of significance is 0 .05 so as you can see we have 2 .2622 so our critical value is 2 .2622.

02:05 So the next thing is for us to slot in our parameters into our formula so we can have our answer.

02:10 So we have the m is equal to 18 .2.

02:13 We have plus or minus.

02:15 Our cv is 2 .26 .22 times our s is 7 .60 divided by the square root of n and our n is 10.

02:24 So we have mew is equal to 18 .2 plus or minus.

02:29 2 .262 times 7 .60 divided by the square root of 10 we have our answer to be 2 .4033...