Question

1. Use the given sample data to find the P-value for the hypothesis test. Round your answer to four decimal places.

x ₁ = 38, n ₁ = 100, x ₂ = 40, n ₂ = 100; H ₀: p ₁ = p ₂, H ₁: p ₁ ≠ p ₂ , α = 0.05

2. A random sampling of 60 pitchers from the National League and 74 pitchers from the American League showed that 38 National and 36 American League pitchers had E.R.A's below 3.5.

Find the test statistic that would be used to test the claim that the proportion of the NL pitchers with E.R.A. below 3.5 is higher than the proportion of the AL pitchers with similar stats.

Round your answer to three decimal places.

3.  Two independent samples are randomly selected and come from populations that are normal. The sample statistics are given below:

n₁ = 47            n₂ = 52
  ₁ = 24.2      ₂ = 18.7
s₁ = 5.0             s₂ = 5.6

Find the standardized test statistic t to test the hypothesis that μ₁ = μ₂.  Round your answer to three decimal places.

Answer 1

1. Test for difference of Proportions:

P-value = 0.7719

Thus we conclude that there is no significance difference between the proportion of two populations

2) H0: The proportion of the NL pitchers with E.R.A. below 3.5 is not higher than the proportion of the AL pitchers

H1: The proportion of the NL pitchers with E.R.A. below 3.5 is higher than the proportion of the AL pitchers

Thus we conclude that the proportion of the NL pitchers with E.R.A. below 3.5 is higher than the proportion of the AL pitchers

3) Test for independent samples:

Thus we conclude that the two population proportions are different