Apol n tes that 43% of a country\'s adults favor a ban on assa it weapons. Suppo

Question

Apol n tes that 43% of a country's adults favor a ban on assa it weapons. Suppose 310 adults in a cena egion are randomly sun eyed and 149 say they favor a ban. Based on this sample, test using alpha -001 whether the proportion of the region's residents who favor the ban is diflerent from the proporion given in the poll for the country as a whole. Repor the p-value for this hypothesis test identify the null and altenative hypotheses for this test. Let p be the population proportion of the region's residents who favor a ban on assault weapons OA. Ho:p#0.43 HA: p-o.43 HA: p#043 A p 0.43 MA P043 Perform the test using a normal approximation. Identify the test statistic. (Rbund to two decimal places as needed.) identify the p-value (Round to three decimal places as needed ) Stnte the conclusion for this hypothesis test. residents who favor a ban crn y|H suficient evidence at the ?-o01 level of significan e t conclude that the population proportion of . There assault weapons is

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.43
Alternative hypothesis: P ? 0.43

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (?) and compute the z-score test statistic (z).

? = sqrt[ P * ( 1 - P ) / n ]

? = 0.02812
z = (p - P) / ?

z = 1.801

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -1.80 or greater than 1.80.

Thus, the P-value = 0.072

Interpret results. Since the P-value (0.0719) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Reject H0, There is not sufficient evidence at the alpha = 0.01 level of significance to conclude that the population proportion of the region's residents who favor the ban is assault weapon is different from the proportion given in the pool for the country as a whole.

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