# part b

**Topics:**Statistical hypothesis testing, Statistics, Statistical inference

**Pages:**4 (899 words)

**Published:**February 26, 2014

a. The average (mean) annual income was less than $50,000

Null Hypothesis: The average annual income was greater than or equal to $50,000 H₀: µ > 50000

Alternate Hypothesis: The average annual income was less than $50,000. Ha: µ > 50000

Analysis Plan: Significance Level, α=0.05.

Since the sample size, n > 30 I will use z-test for mean to test the given hypothesis. As the alternative hypothesis is Ha: µ > 50000, the given test is a one-tailed z-test. Critical Value and Decision Rule:

The critical value for significance level, α=0.05 for a lower-tailed z-test is given as-1.645. Decision Rule: Reject H₀, if z – statistic, -1.645

Test Statistic - minitab

One-Sample Z: Income ($1000)

Test of mu = 50 vs < 50

The assumed standard deviation = 14.55

95% Upper

Variable N Mean StDev SE Mean Bound Z P

Income ($1000) 50 43.48 14.55 2.06 46.86 -3.17 0.001

Interpretation of Results and Conclusion:

Since the P-value (0.0001) is smaller than the significance level (0.05), we reject the null hypothesis. The p-value implies the probability of rejecting a true null hypothesis. The significance level of 0.05, there is enough evidence to support the claim that the average annual income was less than $50,000. Confidence Interval - minitab

One-Sample Z

The assumed standard deviation = 14.55

N Mean SE Mean 95% CI

50 43.48 2.06 (39.45, 47.51)

The 95% upper confidence limit is 47.51. Since, 50.00 lies beyond the 95% upper confidence limit, we can support the claim that the average annual income was less than $50,000.

b. The true population proportion of customers who live in an urban area exceeds 40% . Null Hypothesis: The true population proportion of customers who live in an urban area is less than or equal to 40%. H₀: p < 0.40

Alternate Hypothesis: The true population proportion of customers who live in an urban area is greater than 40%. Ha: p > 0.40

Analysis Plan: Significance Level, α=0.05 and...

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