How, if at all, would your answer to part (a) change if the sample consisted of

Question

How, if at all, would your answer to part (a) change if the sample consisted of 160 white herons and 30 blue herons? At a particular hospital, there were a total of 681 births over a 6-month period. Of these, 233 occurred on weekend days (Saturday and Sunday). The goal of this problem is to determine whether these data indicate that births occur as often on weekends as mere chance would predict. (a) If births occur randomly throughout the week with no preference for one day over another, what proportion p would be expected to occur on weekends? (b) At the 0.01 level of significance, test whether births occur more often on weekends than mere chance would predict. (c) What is the P-value of the test? Some studies have suggested that exposure to allergens during infancy may predispose a child to later allergic disease. Other studies indicate the opposite effect. A study was conducted to investigate the relationship between early exposure of children to dogs and later allergic sensitization. In the study, 184 children who had some exposure to dogs during their first year of life were compared to 220 children who had not been exposed to dogs before their first birthday. All children were given a skin test between their sixth and seventh birthdays. The results were that 6 of the children

Explanation / Answer

Q.2 (a) Proportion of births expected to be occur on weekends as there is no preference of any day over other.

p = 2/7 = 0.286

(b) Null Hypothesis : H0 : p = p0 = 0.286

Alternative Hypothesis : Ha p > p0 = 0.286

Test statistic

Proportion = 233/681 = 0.3421

standard error of proportion se0= sqrt [ p0 (1-p0)/N] = sqrrt [2/7 * 5/7 * 1/ 681] = 0.0173

Z = (p - p0)/ se0 = (0.3421 - 0.286)/ 0.0173 = 3.243

so for alpha = 0.01 and Zcr = 2.33

so here Z > Zcr so we can reject the null hypothesis.

Here p - value = 0.0006 < 0.01

so we can conclude that people prefer their child birth on holidays.

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