Question

A random sample of 25 inpatients in a hospital had a mean healthcare expenditure of $2000 and standard deviation of $300. Use these values to test the following hypotheses at α = 0.01:

(a) whether or not the mean healthcare expenditure among all inpatients in the hospital is less than $2300.

(b) whether or not the mean healthcare expenditure among all inpatients in the hospital is different from $2100.

Answer 1

Solution :

a ) Given that

= 2300

=2000

S =300

n = 25

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 2300

Ha : < 2300

Test statistic = t

= ( - ) / S / n

= (2000 -2300) / 300 / 25

= -5.0

Test statistic = t= -5.0

P-value = 0.00002

= 0.01

P-value <

0.00002 <0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that   

b ) Given that

= 2100

=2000

S =300

n = 25

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 2100

Ha : 2100

Test statistic = t

= ( - ) / S / n

= (2000 -2100) / 300 / 25

= -1.667

Test statistic = t=  -1.667

P-value =0.1085

= 0.01

P-value >

0.1085 > 0.01

Do not reject the null hypothesis .

There is insufficient evidence to suggest that