Question

Humans are known to have a mean gestation period of 280 days (from last menstruation) with a standard deviation of about 9 days. A hospital wondered whether there was any evidence that their patients were at risk for giving birth prematurely. In a random sample of 70 women, the average gestation time was 277.7 days. Is the alternative hypothesis one-sided or two-sided? (type your choice as either one-sided or two-sided) What is the value of the test statistic? (round to 3 decimal places) What is the P-value of the test? (round to 3 decimal places) What is the conclusion of the test if alpha is 0.05? (type your choice as either reject or fail to reject)

Answer 1

Solution :-

Givan that ,

= 280  

= 277.7

= 9

n = 70

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 280

Ha :    280

Test statistic = z

= ( - ) / / n

= ( 277.7 - 280 ) / 9 / 70

= -2.138

The test statistic = -2.138

P - value = 2 * P ( Z < -2.138 )

= 2 * 0.0163

= 0.0326

= 0.033

P-value = 0.033

= 0.05  

0.033 < 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to claim