Calculation practice: Normal approximation to a binomial test. From 1995 to 2008 in the United States, 531 of the 648 people who were struck by lightning were men. Test whether this proportion is different from the 50% that might be expected by the proportion of men in the population as a whole (Avon 2009). Use the binomial test with a normal approximation.

a. State the null hypothesis for this binomial test.

b. Calculate the mean of the null distribution for the number of men struck by lightning under this null hypothesis.

c. What is the standard deviation of the distribution for the number of men hit by lightning under the null hypothesis?

d. Is your target value (531) above or below the value given by the null hypothesis? If above, subtract one-half from that target for the continuity correction. If below, add a half for the continuity correction.

e. What is the standard normal deviate (Z) for the continuity-corrected observed number of men, using the mean and standard deviation calculated in parts (b) and (c)?

f. What is the probability under the normal distribution of getting a result of 531 or greater (including the continuity correction)?

g. What is the two-tailed P-value for this binomial test?

h. State the conclusion from your test.

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