[college intro statistics] simple problems. please answer #5 and #6. Show your w
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[college intro statistics] simple problems. please answer #5 and #6. Show your work in detail thanks!
5. It is said that more males register to vote in a national election than females. A research organization selected a random sample of 300 registered voters and reported that 165 of the registered voters were male. Using the p-value approach, can you conclude that more males registered to vote than females? Use =0.05. 6. A 95% confidence interval to estimate the true mean difference of x-4, was calculated to be (2, 10) when using a pooled procedure (assuming the population variances are equal) from Normal random samples of nx 25 and 37. Calculate the test statistic to determine whether Ho x-y 0 is appropriate.Explanation / Answer
Solution:-
5)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.50
Alternative hypothesis: P > 0.50
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. 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 ]
= 0.02887
z = (p - P) /
z = 1.73
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 one-tailed test, the P-value is the probability that the z-score is more than 1.73. Thus, the P-value = 0.0418
Interpret results. Since the P-value (0.0418) is less than the significance level (0.05), we cannot accept the null hypothesis.
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