What is the value of m
2 answers:
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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.
Answer:
The boat is approaching the dock at rate of 2.14 ft/s
Step-by-step explanation:
The situation given in the question can be modeled as a triangle, please refer to the attached diagram.
A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow that means x = 5 ft.
The length of rope from bow to pulley is 13 feet that means y = 13 ft.
We know that Pythagorean theorem is given by
Differentiating the above equation with respect to time yields,
dx/dt = 0 since dock height doesn't change
The rope is being pulled in at a rate of 2 feet per second that is dz/dt = 2 ft/s
First we need to find z
z² = (5)² + (13)²
z² = 194
z = √194
z = 13.93 ft
So,
Therefore, the boat is approaching the dock at rate of 2.14 ft/s
