Question

A hospital claims that the proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 48%. In a random sample of 200 babies born in this hospital, 76 weighed over 7 pounds. Is there enough evidence to reject the hospital's claim at the 0.01 level of significance? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. H, :p = 0.48 u 0 The null hypothesis: Đ The alternative hypothesis: H, :p = 0.48 O=D Z Oso The type of test statistic: 020 +0 <D O>O The value of the test statistic: (Round to at least three decimal places.) The two critical values at the 0.01 level of significance: (Round to at least three decimal places.) n and Can we reject the claim that the proportion of full- term babies born in their hospital that weigh more than 7 pounds is 48%? Yes Ο Νο

Answer 1

Test statistic Z

Z = ( p ^ - p)/sqrt [ p *(1-p)/n ]

Where p^ = 76/200 = 0.38

Z = ( 0.38 - 0.48)/Sqrt [ 0.48*0.52/200]

Z = -2.831

This is Test statistic value

Now critical values for a = 0.01 and two tailed test

Zcritical = Z​​​​​​a/2  = Z​​​​​​0.005

Zcritical = -2.58 ,