Question

The mean survival time for patients with a particular form of disease is 4 years. A new treatment is tried on 20 patients with this particular disease and their average survival time is 4.7 years with a standard deviation of 1.5 years.

(a) State the direction of the alternative hypothesis to test if the new treatment constitutes a significant improvement in survival time. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box .

(b) State the critical value to conduct the test at 5% level of significance (three decimal places). Type only the numeric value in the box . (No need to specify whether it is t_crit or Z_crit)

(c) What is the calculated test statistic (three decimal places)? Type only the numeric value in the box . (No need to specify whether it is t_calc or Z_calc.)

(d) If the sampling error for a 90% confidence interval was required to be no more than 9 months, how large a sample would be necessary? (Assume 1.5 years is a good estimate of population standard deviation.) Type only the numeric value in the box .

Answer 1

Solution:-

(a) Here the direction is on positive side .

Answer is greater than.

Years

years

(b)

Here sample size is  n = 20

Degree of freedom =

df= n-1 = 20 - 1

df=19

critical value

(c)

Here standard error

Stabdard Error=.3354

(d)

Margin of error =9 months = 0.75 year

sample size = n

critical value = NORMSINV(0.50 + 0.90/2) = 1.645

n = 10.82 or n = 11

answered by: anonymous