Question

A Coin is tossed 1000 times and 545 heads appear. At ? = .01, test the claim that this is not a biased coin. a.) State the null and alternative hypotheses. b.) Verify that the requirements are met for conducting the hypothesis test. c.) Conduct the test of hypothesis by using a P-value.

Answer 1

b) required conditions :-

1. The sampling method must be simple random sampling.
2. Each sample point has only two possible outcomes. head and tail
3. The sample includes at least 10 successes and 10 failures.
4. The population size is at least 20 times as big as the sample size.

a and c part:-

if coin is not biased then 50% times head appears.

The following information is provided: The sample size is N = 1000, the number of favorable cases is X = 545, and the sample proportion is õ= x 0.545, and the significance level is a = 0.01 545 1000 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho:p= 0.5 Ha:p # 0.5 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 = 0.01, and the critical value for a two-tailed test is ze = 2.58. The rejection region for this two-tailed test is R= {z: 121 > 2.58} (3) Test Statistics The Z-statistic is computed as follows: z = p – Po po(1 – po)/n 0.545 – 0.5 10.5(1 – 0.5)/1000 2.846 (4) Decision about the null hypothesis 2.846 > 2c 2.58, it is then concluded that the null Since it is observed that 2 hypothesis is rejected. Using the P-value approach The p-value is p = 0.0044, and since p = 0.0044 < 0.01, it is concluded that the null hypothesis is rejected. (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 different than po, at the a = 0.01 significance level.

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