A random sample of 820 births included 435 boys. Use a 0.05 significance level t

Question

A random sample of 820 births included 435 boys. Use a 0.05 significance level to test the claim that 50.5% of newborn babies are boys. Do the results support the belief that 50.5% of newborn babies are boys? Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is Round to two decimal places as needed.) Identify the P-value for this hypothesis test. The P-value for this hypothesis test is Round to three decimal places as needed.) Identify the conclusion for this hypothesis test. O A. 0 B. O c. O D. Reject Ho. There is not sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys. Fail to reject Ho. There is not sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys. Reject Ho. There is sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys. Fail to reject Ho . There is sufficient evidence to warrant rejection of the claim that 50.5% of newborn babies are boys.

Explanation / Answer

One Proportion z test

Given,

Poportion of boys in sample (p) = 435/820 = 0.5305

Null and Alternate Hypothesis:

H0: p = 0.505 (proportion of boys is 0.505)

Ha: p > 0.505 (proportion of boys is greater than 0.505)

Alpha = 0.05

Test Statisc(z) = (p – p0 )/( p0*(1- p0)/n)1/2 = (0.5303 – 0.505 )/( 0.505*(1- 0.505)/820)1/2 = 1.46

Using the z-table,

p-value =P(z>1.46) = 1-P(z<1.46) = 1-0.9279 = 0.0721

Since, the p-value is greater than 0.05, data is not statistically significant at alpha = 0.05 and we fail to reject the null hypothesis.

Option B

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