Putting It Together: Lupus Based on historical birthing records, the proportion

Question

Putting It Together: Lupus Based on historical birthing records, the proportion of males born worldwide is 0.51. In other words, the commonly held belief that boys are just as likely as girls is false. Systematic lupus erythematosus (SLE), or lupus for short, is a disease in which one's immune system attacks healthy cells and tissue by mistake. It is well known that lupus tends to exist more in females than in males. Researchers wondered, however, if families with a child who had lupus had a lower ratio of males to females than the general population. If this were true, it would suggest that something happens during conception that causes males to be conceived at a lower rate when the SLE gene is present. To determine if this hypothesis is true, the researchers obtained records of families with a child who had SLE. A total of 23 males and 79 females were found to have SLE. The 23 males with SLE had a total of 23 male siblings and 22 female siblings. The 79 females with SLE had a total of 69 male siblings and 80 female siblings. Source: L.N. Moorthy, M.G.E. Peterson, K.B. Onel, and T.J.A. Lehman. "Do Children with Lupus Have Fewer Male Siblings" Lupus 2008 17:128-131, 2008. (a) Explain why this is an observational study. (b) Is the study retrospective or prospective? Why? (c) There are a total of 23+69 92 male siblings in the study. How many female siblings are in the study? (d) Draw a relative frequency bar graph of gender of the siblings. (e) Find a point estimate for the proportion of male siblings in families where one of the children has SLE (f) Does the sample evidence suggest that the proportion of male siblings in families where one of the children has SLE is less than 0.51, the accepted proportion of males born in the general population? Use the = 0.05 level of significance

Explanation / Answer

Part a

This is an observational study because this study is only based on the observations or birthing records. No any experiment is conducted for this study.

Part b

This is a retrospective study because all estimates for this study are based on previous observations or records.

Part c

There are a total of 22 + 80 =102 female siblings in the study.

Part d

Relative frequency bar graph is given as below:

Part e

We are given

Total number of male siblings = 92

Total number of female siblings = 102

Total number of siblings = 92 + 102 = 194

Point estimate for proportion of male siblings = 92/194 = 0.474227

Part f

Here, we have to use z test for population proportion. The null and alternative hypothesis for this test is given as below:

H0: p = 0.51 versus Ha: p < 0.51

This is a lower tailed or left tailed test. (One tailed test)

We are given

= 0.05

n = 194

x = 92

P = x/n = 92/194 = 0.474227

Test statistic = Z = (P – p) / sqrt(pq/n) where, q = 1 – p = 1 – 0.51 = 0.49

Test statistic = Z = (0.474227 - 0.51) / sqrt(0.51*0.49/194)

Test statistic = Z = -0.99672

P-value = 0.1594

P-value > = 0.05

So, we do not reject the null hypothesis.

There is insufficient evidence to conclude that the proportion of male siblings in families where one of the children has SLE is less than 0.51.

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