In a previous year, 61% of females aged 15 years of age and older lives alone. A

Question

In a previous year, 61% of females aged 15 years of age and older lives alone. A sociologist test weather this percentage is different by conducting a random sample of 400 females aged 15 years of age and older and finds that 252 are living alone. Is there sufficient evidence at the alpha = 0.05 level of significance to conclude the proportion has changed? Identify the null and alternative hypotheses for this test. A. H_0: p = 0.61 H_1: p notequalto 0.61 B. H_0: p > 0.61 H_1: p = 0.61 C. H_0: p notequalto 0.61 H_1: p = 0.61 D. H_0: p = 0.61 H_1: p > 0.61 E. H_0: p

Explanation / Answer

The statistical software output for this problem is:

One sample proportion hypothesis test:
p : Proportion of successes
H0 : p = 0.61
HA : p 0.61

Hypothesis test results:

Hence,

Null and alternative hypotheses:

Option A is correct.

z = 0.82

p - value = 0.412

Conclusion:

Option C is correct.

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 252 400 0.63 0.024387497 0.82009237 0.4122

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