Question

4. A random sample of 860 births at St. Jude’s Hospital included 426 boys. The national proportion of newborn boy babies is 51.2%. Use a 0.01 significance level to test the claim that the proportion of newborn boy babies at this hospital is different than the national average.

a. Draw a normal curve for the sampling distribution for samples of size 860 births. Label the mean and the values for one, two and three standard deviations above and below the mean.

Answer 1

4) H₀: P = 0.512

    H₁: P 0.512

= 426/860 = 0.495

The test statistic z = ( - P)/sqrt(P(1 - P)/n)

                            = (0.495 - 0.512)/sqrt(0.512 * (1 - 0.512)/860)

                            = -0.997

At alpha = 0.01, the critical values are z_0.005 +/- 2.575

Since the test statistic value is not less than the negative critical value(-0.997 > -2.575), so we should not reject H₀.

At 0.01 significance level, there is not sufficient evidence to support the claim that the proportion of newborn boy babies at the hospital is different than the national average.

a) = p = 0.512

   = sqrt(p(1 - p)/n)

        = sqrt(0.512(1 - 0.512)/860)

       = 0.017