Question

Data on the numbers of hospltal admissions resuting trom motor vehicle crashes are given below tor Fridays on the 6th or a month and Fridays on the following 13m ofthe same month. Assume that the paired sample data is a simple random sample and that the differences have a distributo al s ao o male normal or struct a confidence nierval estrnate ฎ the mean of the opulaion o d merences bel een hospital a r ssicns se lhe con den e inter to test the Claim that en lhe 1 h cay o a month ais on a Frida the num ters of r cs al admissions rom mator vehice rrashes are nat alected 12 15 Friday the Sth Friday be issions on F day the 13th Find the 95% confidence n c val. on Friday the 5th m nus he nu of hospital ad dcnnod as the number hospital ad ons f data, where cac i vidual dime e co d can value or the dmero es d or the population o all par In this exampl is c (Round to two decimal paccs as ncedcd)

Please read the instruction carefully, I have submitted this question for a lot of times and they were all wrong. Thank you!!

Answer 1

Solution:

x1	x2	d = x1-x2
12	12	0
11	11	0
4	15	-11
8	14	-6
8	12	-4
	Mean	-4.2
	Std. dev	4.604346

We calculate the mean using excel function =AVERAGE and sample standard deviation using excel function = STDEV.S

Degrees of freedom, df = n - 1 = 5 - 1 = 4

Level of significance, $\alpha$ = 0.05

Using t-tables, the critical value at $\alpha$ = 0.05 with df = 4 is given by

t (0.05/2, 4) = t (0.025, 4) = $\pm$2.776

First, we calculate the margin of error,

α.12

2.776*4.604/$\sqrt{}$5

E = 5.717

95% confidence interval is given by:-

$\bar{}$$\bar{d}\pm E$

-4.2 $\pm$5.717

-9.917, 1.517

-9.92 < $\mu_{d}$ < 1.52