Question

P align="center Inference about a Population Propor- tion /p hr Due: 07/01/2019 at 11:59pm EDT hrStudents will be able to: iUL ili;, Perform a hypothe- sis test on population proportion /li ili; Cakculate a confidence interval for a population proportionAi Interpret levels of significance/i il Perform a hypothesis test using a critical value UL hr Functions and symbols that WeBWorK understan ds br Links to some useful WeB WorK pages for students by chance alone. Suppose p is the true proportion of the time Albert will roll a 3 (a) State the null nd atemative hypotheses for testing A bert's dlaim. Type the symbol "p" for the population proportion, whichever symbols you need of "". "". "=", "not " and ex- press any values as a fraction e.g. p= 1/3. Ho H,- (b) Now suppose Albert makes n = 30 rolls, and a 3 comes up 6 times out of the 30 rolls. Detemine the Pvalue of the test: Pvalue (c) Answer the question: Does this sample provide evidence at the 5 percent level that Albert rolls a 3 more often than you'd expect? 1. ( point) Phys icians at a clinic gave what they thought were drugs to 850 patients. Akhough the doctors later learned that the drugs were really placebos, 59 % of the patients re- ported an improved condition. Assume that if the placebo is ineffective, the probability of a patiemt's condition improving is 0.55. Test the hypotheses that the proporticn of patiemts im proving is> 05s (Type: Yes or No) Anwerts) bined (incorтect) 4. (2 points) A newspaper conducted a statewide survey con- cerning the 1998 race for state senator. The newspaper took a SRS of n1100 registered voters and found that 570 would Find the test statis tic: vote for the Republican candidate. Let p represent the propor- tion of registered voters in the state who would vote for the Re- publican candidate. We test Ho p 0.50 H, p>0.50 (a) What is the z-statis tic for this test? Find the Pvalue P Aswerts) bed (b) What is the Pvalue of the test? Anweris) subined (incorrect) (incorrect) 2. (2 points) An article in the Washington Post on March 16 5. (2 points) A noted psychic was tested for ESP. The psy- chic was presented with 260 cards face down and was asked to 1993 stated that nearly 45 percent of all Americans have brown cyes. A random sample of n76 Americans found 28 with brown eyes detemine if the card was one of 5 symbols: a star, cross, cir- clk, square, or three wavy lines. The psychic was correct in 70 cases. Let p represent the probability that the psychic comectly identifies the symbol on the card in a random trial Assume the 260 trials can be treated as an SRS from the population of all guesses We test Ho: p45 H:p 45 (a) What is the 2-statistic for this test? (b) What is the Pvalue of the test? Aswerts) submined To see if there is evidence that the psychic is doing better than just guessing, we test Ho: p 0.2 H p>02 (a) What is the z-statis tic for this test? (b) What is the Pvalue of the test? (incorrect) Amweris) ned 3. (4 points) Albert thinks that he has a special relationship with the number 3. In particular. Abert thinks that he would roll a 3 with a fair 6-sided die more often than you'd expect

plesse help with explanations and answers for all of those ... im stuck and cant figure out how to do them. its the hard copy from web work wnd they are all incorrect.

Answer 1

First two solved. Please post remaining as a seperate question.

1.

850, the number of favorable cases is 0.5894, and the significance level is a= The following information is provided: The sample size is N X 501, and the sample proportion is p 501 850 0.05 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho p 0.55 Ha p 0.55 This corresponds to a used right-tailed test, for which a z-test for one population proportion needs to be (2) Rejection Region Based on the information provided, the significance level is a 0.05, and the critical value for a right-tailed test is e = 1.64 The rejection region for this right-tailed test is R {z : z> 1.64 ( 3 ) Test Statistics The z-statistic is computed as follows: 0.5894 0.55 P po 2.31 VPo(1-po)/n V0.55(1-0.55)/850 (4) Decision about the null hypothesis Since it is observed that z 2.31> e = 1.64, it is then concluded that the null hypothesis is rejected Using the P-value approach: The p-value is p 0.0105, and since p 0.0105 concluded that the null hypothesis is rejected. 0.05, it is (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is greater than p, at the a - 0.05 significance level.

2.

The following information is provided: The sample size is N 76, the number of favorable cases is X 28, and the sample proportion is p 0.3684, and the significance level is 0.05 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho p 0.45 Ha: p 0.45 This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used (2) Rejection Region Based on the information provided, the significance level is a 0.05, and the critical value for a two- tailed test is 1.96 The rejection region for this two-tailed test is R z: z> 1.96 (3) Test Statistics The z-statistic is computed as follows: P po Po (1 po)/n 0.3684 0.45 1.43 V0.45(1-0.45)/76 (4) Decision about the null hypothesis 1.96, it is then concluded that the null hypothesis is not Since it is observed that z1.43< rejected Using the P-value approach: The p-value is p 0.1528, and since p 0.1528> 0.05, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is different than po, at the a 0.05 significance level.