Chapter 7 Analyzing proportions even which eye opens first. One study wanr to me

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Chapter 7 Analyzing proportions even which eye opens first. One study wanr to measure whether fetal testosterone affected how attractive these female micew to male mice as adults (vom Saal and B 1980). Twenty-four male mice were a choice between a female that was OM and another unrelated female that was 2M. (Bo males and females were randomly chosen from their populations.) Each male was placed on platform, and he could jump into the cage of whichever female he preferred. Nineteen of the 24 males chose the 0M female. change the estimated proportion? Would levels it change the confidence interval? How? were (You don't need to do the calculations-just answer qualitatively.) 9. As our planet warms, as it has done for the last century or so, the change in temperature will have major effects on life. There are basically three possibilities for what might happen to a species: it can evolve to be better adapted to the new temperature, it can move closer to the poles so that it experiences temperatures closer to what it has experienced in the past, or it can go extinct. There have been a large number of studies of the second possibility. A recent study of the range limits of European butterflies found that, of 24 species that had changed their ranges in the last 100 years, 22 of them had moved further north and only two had moved further south (Parmesan et al. 1999). Assume that these 24 are a random sample of butterfly species with altered ranges. Test the hypothesis that the fraction of butterfly species moving north is dif ferent from the fraction moving south Oviduct OM Placenta sac 10. Imagine that there were two studies of the prev alence of melanism (solid black coat color). One estimated that the proportion of black leopards in this population was 52%, with a 95% confi dence interval that ranged from 46% to 58 The other study estimated the proportion to be 64% with a 95% confidence interval that ranged from 35% to 85% a. Which study most likely had a larger sample a. Is this evidence that the males prefer one type of female over the other? b. If the two females presented to each male a given trial had been sisters, would this have been a better or worse experimental desig b. Which estimate is more believable? 11. Mice have litters of several pups at once. The 12. A giant vat contains large numbers of two types pups are arranged in a line within the mother's uterus, so many fetuses lie between two of their siblings. It has been shown that female fetuses located between two male fetuses (2M) experience higher testosterone levels than those adjacent to no male fetuses (OM), because the hormone is produced by the males and diffuses across the fetal membranes and through the amniotic fluid to adjacent females. The higher fetal testosterone levels are known to have sev- eral effects on the females later in life, includin increased aggression levels, growth rates, and of bacteria, called strain A and strain B. Assune that 30% of the bacteria in the vat are strain and the other 70% are strain B. The vat mixed. Twenty technicians each collect a ra dom sample of 15 cells from the vat and the determine which strain each cell bel a. What will the proportion of stra 1s, in these 20 samples, on averagef b. Each technician counts the number A bacteria cells in his or her sample. distribution should the number of stra bacteria in samples conform?

Explanation / Answer

9.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis

Null hypothesis H0 : The fraction of butterfly species moving north is same as the fraction moving south. P1 = P2 = 0.5
Alternative hypothesis Ha : The fraction of butterfly species moving north is different than the fraction moving south. P1 P2

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

p1 = 22/24 = 0.9167

p2 = 2/24 = 0.0833

Let P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Hypothesized proportion, P = 0.5

= sqrt[ P * ( 1 - P ) / n ] = sqrt [(0.5 * 0.5) / 24] = sqrt(0.01042) = 0.1021

z = (p1 - P) / = (0.9167- 0.5)/0.1021 = 4.08

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -4.08 or greater than 4.08.

We use the Normal Distribution Calculator to find P(z < -4.08) = 0.00002, and P(z > 4.08) = 0.00002. Thus, the P-value = 0.00002 + 0.00002 = 0.00004.

Interpret results. Since the P-value (0.00004) is less than the significance level (0.05), we reject the null hypothesis.

And conclude that there is statistical significance that the fraction of butterfly species moving north is different than the fraction moving south. P1 P2

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