Question

A random sample of 12 paired observations indicated a correlation of 0.32. Can we

conclude that the correlation in the population is equal to zero? Use 0.05 level of

significance. (3 marks)

j. The following is a list of hospitals in Kenya.

ID

NO

Name Address

01 St. Luke Hospital 1140, Kisumu

02 Matter Hospital 1256, Nakuru

03 KNH 1000, Nairobi

04 Thika Level 5 1416, Thika

05 Consolata General

Hospital

3120,

Mombasa

06 Eldoret Referral 1127, Eldoret

07 Children Psychiatric

Hospital

2123, Kisumu

i. A sample of three hospitals is to randomly selected. The random numbers are

09, 02, 05, 10, 00, 07. Which hospitals are included in the sample?

(3 marks)

ii. A sample is to contain every second location. We select 01 as the starting

point. Which hospitals will be included in the sample? (3 marks)

Answer 1

i.

There exist hospitals with numbers 02, 05, 07. So, answer is:

02 Matter Hospital 1256, Nakuru

05 Consolata General Hospital 3120, Mombasa

07 Children Psychiatric Hospital 2123, Kisumu

ii)

Numbers are 01, 03, 05, 07. So, answer is:

01 St. Luke Hospital 1140, Kisumu

03 KNH 1000, Nairobi

05 Consolata General Hospital 3120, Mombasa

07 Children Psychiatric Hospital 2123, Kisumu

$H_0: r=0$ , correlation coefficient is not significantly different from zero

$H_a: r\neq0$ , correlation coefficient is significantly different from zero

test statistic:

$t=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}=\frac{0.32\sqrt{12-2}}{\sqrt{1-0.32^2}}=1.068$

$df=12-2=10$

critical value:

$t_{crit}=2.228$

Since $t<t_{crit}$ we accept null hypothesis. The correlation in the population is equal to zero.