Question

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A survey of 848 Americans found that 441 do not believe President Trump’s assertion that there is a crisis on the Mexican-US border. (https://www.independent.co.uk/news/world/americas/us-politics/trump-shutdown-latestborder-wall-poll-support-tweets-republicans-democrats-graham-pelosi-a8726206.html)

(a) As a Democrat, you believe that a majority of Americans do not believe Trump’s assertion of a crisis at the US-Mexican border and want to confirm your belief. Perform a test at the 0.05 level of significance using a manual calculation of the appropriate (1-sided) confidence interval for the proportion of Americans who do not believe Trump. What is your conclusion?

(b) Suppose you wanted to take a large enough sample size to enable you to conclude with the same level of significance that more than 50% of Americans do not believe Trump’s assertion of a crisis. What sample size would be required?

(c) To test whether the proportion of college students who do not believe Trump exceeds 50%, you found 13 out of a small sample of 15 randomly selected college students who do not believe Trump. Perform the test, using the 0.05 level of significance and show how you would calculate the p-value for this test.

Answer 1

From the given information. x-441 and n a) The sample proportion is, 848 441 848 0.520047 -0.52 (Round to 2 decimal place) Calculate the 95% lower confidence limit. From the standard normal tables, the Z-critical value at the 95% confidence level is: 1.645. Lower limit = p± Zentai 11p(1-p) 0.52(1-0.52) 848 0.52 t1.645 = 0.52 ±0.02 8222 0.491778 Conclusion: The 95% lower confidence limit is less than the 0.5, we fail to reject the null hypothesis and conclude that more than 50% of Americans do not believe Trump's assertion of a crisis.

b) Calculate the sample size. (1.645) (0.52(1-0.52) (0.5-0.52) 2.706025 (0.2496) 0.0004 0.675424 0.0004 1688.56 1689 (Round to nearest next number) c) From the given information, x-13 andn-15 The sample proportion is, 13 15 0.866667 0.87(Round to 2 decimal place) Null hypothesis, Ho p 0.50 Alternative hypothesis, H: p> 0.50 Level of significance, a 0.0.5

Calculate the test statistic value p-p p(1-p) 0.87-0.50 0.50 (1-0.50) 15 - 2.84 Calculate the P - value P-value - P(Z> Zo) -1- P(Z s2.84) -1--NORMSDIST(2.84)(Use MS Excel function) = 1-0.997744 0.002256 Conclusion: The P-value is less than the given significance level 0.05, so we reject the null hypothesis and conclude that the proportion of college students who do not believe Trump exceeds 50% at the 0.05 level of significance