A professor is examining a new strain of bacteria. The amount of bacteria can be modeled by function s(n) = 20 · bn, where n is
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The usual expectation for this kind of experiment is that the peas would yield green and yellow peas in a 3:1 ratio, or 75% green to 25% yellow. So your null hypothesis is that the proportion of yellow peas is 
.
You're testing the claim that 26% of the offspring will be yellow, which means the alternative hypothesis is that the proportion of yellow peas is actually 0.26, or more generally that the expected proportion is greater than 0.25, or
.
The test statistic in this case will be
where
is the proportion assumed under the null hypothesis, 
is the measured proportion, and 
is the sample size. You have 
, 
, and 
, so the test statistic is
Because you're testing
, this is a right-tailed test, so the P-value is
The critical value for a right-tail test at a 0.05 significance level is
, which means the rejection region is any test statistic that is larger than this critical value. Since 
in this case, we reject the null hypothesis.
So the conclusion for this test is that the sample proportion is indeed statistically significantly different from the proportion suggested by the null hypothesis.
You're testing the claim that 26% of the offspring will be yellow, which means the alternative hypothesis is that the proportion of yellow peas is actually 0.26, or more generally that the expected proportion is greater than 0.25, or
The test statistic in this case will be
where
Because you're testing
The critical value for a right-tail test at a 0.05 significance level is
So the conclusion for this test is that the sample proportion is indeed statistically significantly different from the proportion suggested by the null hypothesis.