Need part F more than the other parts 9. a) b) c) d) e) f) A die is rolled 120 t

Question

Need part F more than the other parts

9. a) b) c) d) e) f) A die is rolled 120 times, it lands five 28 times. Is this evidence statistically significant enough to conclude that the die is not fairly balanced? Use a significance level of 0.01. State the Null and Alternative hypothesis. Draw the picture to state the rejection region for a significance level of 0.05. Find the Test statistic value z. Find the P-value. Decide whether HO should be rejected, and state this conclusion in the problem context. Determine the number of tests required if it is necessary that Beta (25) 0.03.

Explanation / Answer

Solution:-

P = 1/6

P = 0.1667

p = 28/120

p = 0.2333

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

Null hypothesis: P = 0.1667
Alternative hypothesis: P 0.1667

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 0.05. 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 ]

= 0.03402
z = (p - P) /

z = 1.959

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 -1.959 or greater than 1.959.

Thus, the P-value = 0.0501

Interpret results. Since the P-value (0.0501) is greater than the significance level (0.05), we cannot reject the null hypothesis.

e) From the above test we do not have sufficient evidence in the favor of the claim that die is not fairly balanced.

f) Number of tests required to get Beta(25) = 0.03 is 28.

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