In a previous year, 54% of females aged 15 years of age and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 600 females aged 15 years of age and older and finds that 348 are living alone. Is there sufficient evidence at the $\alpha = 0.1$ level of significance to conclude the proportion has changed? Identify the null and alternative hypotheses for this test. A. $H_0: p > 0.54$ $H_1: p = 0.54$ D. $H_0: p = 0.54$ $H_1: p \neq 0.54$ Find the test statistic for this hypothesis test. z = (Round to two decimal places as needed.) B. $H_0: p < 0.54$ $H_1: p = 0.54$ E. $H_0: p = 0.54$ $H_1: p < 0.54$ C. $H_0: p \neq 0.54$ $H_1: p = 0.54$ F. $H_0: p = 0.54$ $H_1: p > 0.54$
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54. The alternative hypothesis is that the proportion is different from 0.54. Show more…
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In a previous year, 56% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 500 females aged 15 and older and finds that 273 are living alone. Is there sufficient evidence at the α = 0.01 level of significance to conclude the proportion has changed? Identify the null and alternative hypotheses for this test. Find the test statistic for this hypothesis test. Determine the P-value for this hypothesis test. State the conclusion for this hypothesis test. Since the P-value is than α, H0. There sufficient evidence at the α = level of significance to conclude that the proportion of females aged 15 and older who are living alone has changed.
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In a previous year, 52% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 650 females aged 15 and older and finds that 345 are living alone. Is there sufficient evidence at the α = 0.05 level of significance to conclude the proportion has changed? Because nPo ≥ 10, the sample size is 5% of the population size, and the sample meets the requirements for testing the hypothesis satisfied (Round to one decimal place as needed): Identify the null and alternative hypotheses for this test: H0: The proportion of females aged 15 and older who live alone is the same as in the previous year. H1: The proportion of females aged 15 and older who live alone has changed. Find the test statistic for this hypothesis test: Z0 = (proportion in sample - proportion in previous year) / standard error of proportion (Round to two decimal places as needed) Determine the P-value for this hypothesis test: P-value = 0.02 (Round to three decimal places as needed) State the conclusion for this hypothesis test: Do not reject H0: There is sufficient evidence at the α = 0.05 level of significance to conclude that the proportion of females who are living alone has not changed. Reject H0: There is sufficient evidence at the α = 0.05 level of significance to conclude that the proportion of females who are living alone has changed.
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In a previous year, 57% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 450 females aged 15 and older and finds that 246 are living alone. Is there sufficient evidence at the α = 0.05 level of significance to conclude that the proportion has changed? Because n * p0 = 450 * 0.57 = 256.5, the sample size is less than 5% of the population size, and the sample is given to be random, the requirements for testing the hypothesis are satisfied. Identify the null and alternative hypotheses for this test: H0: p = 0.57 H1: p ≠ 0.57 Find the test statistic for this hypothesis test: Z = (p̂ - p0) / sqrt(p0 * (1 - p0) / n) Z = (246/450 - 0.57) / sqrt(0.57 * (1 - 0.57) / 450)
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