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1) At a Midwestern hospital there were a total of n = 932 births in 20 consecutive weeks

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1) At a Midwestern hospital there were a total of n = 932 births in 20 consecutive weeks. Consider a binomial test with two categories of births - weekdays and weekends - using a nondirectional alternative. The null hypothesis is that the timing of births is completely random throughout the week; i.e. there is no increase or decrease in the rate of births at weekends.

(a) Let Y be the number of births on weekends out of the n = 932 births. What is the distribution of Y under the null hypothesis?

(b) Out of the 932 births, y = 216 occurred during weekends. What is the sample proportion of births during weekends? What are the odds of giving birth on weekdays, relative to at weekends?

(c) Shown below is the output of the binomial test. Draw conclusion under a significance level of α = 0.05. Exact binomial test data: 216 and 932 number of successes = 216, number of trials = 932, p-value = 0.0002146