Bill Alther is a zoologist who studies Anna\'s hummingbird (Calypte anna referen
ID: 3231868 • Letter: B
Question
Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna referenced from: Hummingbirds, K. Long and W. Alther.) Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows:
3.7, 2.9, 3.8, 4.2, 4.8, 3.1
Let x be a random variable representing weights of Anna's hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and = 0.64 gram. It is known (from previous research) that for the population of all Anna's hummingbirds, the average weight has been 4.70 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.70 grams? Use = 0.05.
(a) Enter the following.
x =
s =
(b) Identify the claim, the null hypothesis, and the alternative hypothesis.
(c) Will you use a left-tailed, right-tailed, or two-tailed test?
left-tailed
right-tailed
two-tailed
(d) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since we assume that x has a normal distribution with unknown .
The standard normal, since n is large with known .
The Student's t, since n is large with unknown .
The standard normal, since n is large with unknown .
The standard normal, since we assume that x has a normal distribution with known .
The Student's t, since we assume that x has a normal distribution with known .
(e) Sketch the sampling distribution showing the area corresponding to the approximate P-value.
(f) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?
At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
(g) State your conclusion in the context of the application.
Fail to reject the null hypothesis, there is sufficient evidence that humming birds in the Grand Canyon weigh less.
Reject the null hypothesis, there is sufficient evidence that humming birds in the Grand Canyon weigh less.
Fail to reject the null hypothesis, there is insufficient evidence that humming birds in the Grand Canyon weigh less.
Reject the null hypothesis, there is insufficient evidence that humming birds in the Grand Canyon weigh less.
Claim: > < = 4.70 Ho: > < = 4.70 H1: > < = 4.70Explanation / Answer
Given that,
population mean(u)=4.7
standard deviation, =0.64
sample mean, x =3.75
number (n)=6
null, Ho: =4.7
alternate,birds in this part of the Grand Canyon is less than 4.70 grams H1: <4.7
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 3.75-4.7/(0.64/sqrt(6)
zo = -3.63596
| zo | = 3.63596
critical value
the value of |z | at los 5% is 1.645
we got |zo| =3.63596 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : left tail - ha : ( p < -3.63596 ) = 0.00014
hence value of p0.05 > 0.00014, here we reject Ho
ANSWERS
---------------
null, Ho: =4.7
alternate, H1: <4.7
test statistic: -3.63596
critical value: -1.645
decision: reject Ho
p-value: 0.00014
At the = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
Reject the null hypothesis, there is sufficient evidence that humming birds in the Grand Canyon weigh less.
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