Question

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2. One of Gregor Mendel’s famous hybridization experiments with peas yielded 580 offspring with 152 of those peas (or 26%) having yellow pods. According to Mendel’s theory, 25% of the offspring peas should have yellow pods. Do the results of the experiment differ from Mendel’s claimed rate of 25% by an amount that is statistically significant? Why or why not?



A)No, because it is unlikely for the results to occur again.


B)No, because the difference does not appear to be significant.


C)Yes, because the difference does not appear to be significant.


D)Yes, because the difference is not large enough for such a large sample.

Answer 1

The results of the experiment do not differ significantly from Mendel's claimed rate of 25%.

Step-by-step explanation:

According to Mendel's theory, 25% of the offspring peas in his experiment should have yellow pods. However, the actual results showed that 26% of the offspring had yellow pods. To determine if the difference is statistically significant, we can use a hypothesis test. The null hypothesis is that the true proportion of peas with yellow pods is 25%, and the alternative hypothesis is that it is not 25%. We can calculate the test statistic, which is the difference between the observed proportion (26%) and the expected proportion (25%), divided by the standard error. With the given sample size and proportions, the test statistic is approximately 0.967.

To determine if this difference is statistically significant, we compare the test statistic to the critical value corresponding to our desired level of significance. If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis. In this case, at a significance level of 0.05, the critical value is around 1.96. Since the test statistic of 0.967 is less than 1.96, we fail to reject the null hypothesis. Therefore, the results of the experiment do not differ significantly from Mendel's claimed rate of 25%.

Answer 2

B)No, because the difference does not appear to be significant.

Step-by-step explanation:

We are given

One of Gregor Mendel’s famous hybridization experiments with peas yielded 580 offspring with 152 of those peas (or 26%) having yellow pods

While Mendel's theory says

25% of the offspring peas should have yellow pods

we know that

25% is close to 26%

so, 26%-25%=1%

we can see that difference is not large or very significant

so, It does not differ much

No, because the difference does not appear to be significant