Question

# Suppose a coin is randomly tossed n = 400 times, resulting in X = 240 Heads....

Suppose a coin is randomly tossed n = 400 times, resulting in X = 240 Heads. Answer each of the following; show all work!

(a) Calculate the point estimate, and the corresponding two-sided 95% confidence interval, for the true probability pi = P(Heads), based on this sample.

(b) Calculate the two-sided 95% acceptance region for the null hypothesis H0: pi = 0.5 that the coin is fair.

(c) Calculate the two-sided p-value (without correction term) of this sample, under the null hypothesis H0: pi = 0.5 that the coin is fair.

(d) Explain below how EACH of your answers in (a), (b), and (c) can be used to conduct a formal test of the null hypothesis, and arrive at a formal “reject or retain” conclusion at the alpha = .05 significance level. Also interpret in the context of this experiment.

• 95% Confidence Interval:

• 95% Acceptance Region:

• p-value:

• Conclusion:

• Interpretation:

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