Question

A researcher is interested in seeing if the average income of rural families is different than that of urban families. To see if his claim is correct he randomly selects 42 families from a rural area and finds that they have an average income of $68532 with a population standard deviation of $832. He then selects 47 families from a urban area and finds that they have an average income of $67140 with a population standard deviation of $809. Perform a hypothesis test using a significance level of 0.10 to test his claim. Let rural families be sample 1 and urban familis be sample 2.

The correct hypotheses are:

• H0:μ1≤μ2H0:μ1≤μ2
  HA:μ1>μ2HA:μ1>μ2 (claim)
• H0:μ1≥μ2H0:μ1≥μ2
  HA:μ1<μ2HA:μ1<μ2 (claim)
• H0:μ1=μ2H0:μ1=μ2
  HA:μ1≠μ2HA:μ1≠μ2 (claim)

Since the level of significance is 0.10 the critical value is 1.645 and -1.645

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

The decision can be made to:

• reject H0H0
• do not reject H0H0

The final conclusion is that:

• There is enough evidence to reject the claim that the average income of rural families is different than that of urban families.
• There is not enough evidence to reject the claim that the average income of rural families is different than that of urban families.
• There is enough evidence to support the claim that the average income of rural families is different than that of urban families.
• There is not enough evidence to support the claim that the average income of rural families is different than that of urban families.

Answer 1

Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 ≠ μ2

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(692224/42 + 654481/47)
sp = 174.375

Test statistic,
z = (x1bar - x2bar)/sp
z = (68532 - 67140)/174.375
z = 7.983

P-value Approach
P-value = 0.000
As P-value >= 0.1, fail to reject null hypothesis.

do not reject H0

There is not enough evidence to support the claim that the average income of rural families is different than that of urban families