Question

1. In the study examining socioeconomic differences in birth weight, the mean birth weight for babies born to n₁=32 mothers with a college education was 2998 grams with a standard deviation of 230 grams, while the mean birth weight for babies born to n₂=41 mothers with no more than a high school education was 2765 grams with a standard deviation of 332 grams. Which of the following states the appropriate hypotheses for testing if the mean birth weight between these two groups of mothers in different, where μ₁=the mean for mothers with a college education and μ₂=the mean mothers with no more than high school education

a. H₀:μ₁ = μ₂ vs. H_a:μ₁ < μ₂

b. H₀:μ₁ = μ₂ vs. H_a:μ₁≠ μ₂

_c. H₀:μ₁ = μ₂ vs. H_a:μ₁ > μ₂

_d. H₀:μ_{1 =} μ₂ vs. H_a:μ₁ > μ

2. continuing from the last question, which of the following is the 95% confidence interval for the difference between the mean birth weight of these two groups of mothers?

For calculating the standard error, use s.e.=sqrt (s₁² + s₁²) + (n₁ + n₂), recalling that s² is the sample varinace, or standard deviation squared.

a. (-33, 279.0)

b. (-1.99, 1.99)

c. (98.78, 367.21)

d. (0.49, 257.0)

Answer 1

1)

Null hypothesis Ho : u1 = u2

Alternate hypothesis Ha : u1 not equal to u2

2)

As the population standard deviation is unknown and we are given with the sample s.d as the best estimate we will use t distribution to estimate the interval

n1 = 32

n2 = 41

Degrees of freedom is = smaller of n1-1, n2-1 = 31

For 31 dof and 95% confidence level, critical value t from.t distribution is = 2.04

Margin of error (MOE) = t*standard error

t = 2.04

S.d = √{(s1^2/n1)+(s2^2/n2}

S1 = 230

S2 = 332

After substitution

MOE = 134.415958275

Interval is given by

(u1-u2)-MOE, (u1-u2)+MOE

u1 = 2998

u2 = 2765

(98.58, 367.42)

Option C is closest