Question

A random sample data is given below for annual income from 30 households.

96727	96621	107235
95366	97681	101890
95432	96697	107511
96886	96522	95385
97469	96664	106627
95744	95208	107795
98717	106622	107338
94929	95801	105601
97912	97611	96362
96244	97835	99610

A. From the info given above, what is the IQR?

B. From the data above, construct a 95% confidence interval for the population's mean annual income. _____________< u > _____________

C. What is the statistical interpretation of this particular confidence interval?

Answer 1

A.

Interquartile range or IQR is given by, IQR = Q3-Q1

Here, Q1= 96273.5

and Q3= 101320

Therefore, IQR = 5046.5

B.

Let the mean and standard deviation are unknown, so we have to estimate them.

Here, the pivotal quantity is, nX-μS ~tn-1, n=30.

The 95% confidence interval for μ is,

(X-S30t0.025;29,X+S30t0.025;29)

Now, from the sample, X=1ni=1nXi=99268.07

and, S=1n-1i=1n(Xi-X)2=4547.495

and, t0.025;29=2.04523

Then, X-S30t0.025;29=98958.04

and, X+S30t0.025;29=99578.09

Therefore, the required 95% confidence interval for μ is, (98958.04,99578.09)

C.

Interpretation:

          We can conclude that the true mean μ of the sample lies in the range

(98958.04,99578.09) with 95% certainty or confidence.