Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† 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 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 1.00 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.75 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.75 grams? Use α = 0.01. (a) What is the level of significance?  State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μ < 4.75 g; H1: μ = 4.75 g; left-tailedH0: μ = 4.75 g; H1: μ < 4.75 g; left-tailed    H0: μ = 4.75 g; H1: μ ≠ 4.75 g; two-tailedH0: μ = 4.75 g; H1: μ > 4.75 g; right-tailed (b)Compute the z value of the sample test statistic. (Round your answer to two decimal places.)  (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Question

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† 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

The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 1.00 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.75 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.75 grams? Use α = 0.01.

(a) What is the level of significance?
  

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
H0: μ < 4.75 g; H1: μ = 4.75 g; left-tailedH0: μ = 4.75 g; H1: μ < 4.75 g; left-tailed    H0: μ = 4.75 g; H1: μ ≠ 4.75 g; two-tailedH0: μ = 4.75 g; H1: μ > 4.75 g; right-tailed


(b)Compute the z value of the sample test statistic. (Round your answer to two decimal places.)
  

(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
  

Expert Answer

1 Rating

Want to see the step-by-step answer?

See Answer

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

See Answer
*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects.
Tagged in

Related Statistics Q&A

Find answers to questions asked by student like you

Q: The same media consultants decided to continue their investigation of the focal relationship between...

A: In this question, the statistical summary about three models represented by three equation has given...

Q: The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate co...

A: Hi, since the problem posted by you contains multiple sub-parts, we are answering the first three su...

Q: 2. The following table represents the carbon emissions in millions of tons from consumption of fossi...

A: (a) Point estimate and standard deviation:Point estimate:The general formula to obtain the mean of a...

Q: A grocery store manager did a study to look at the relationship between the amount of time (in minut...

A: The estimated regression line is as follows:

Q: Make a frequency table, a pie chart, and a bar plot for the following data for patients' blood types...

A: Frequency distribution:The number of times each value of X repeats is the frequency of that particul...

Q: Consider a drug testing company that provides a test for marijuana usage. Among 301 tested subjects,...

A: Given hypothesis testp be the proportion of wrong test results Null hypothesis : p = 0.10Alternate H...

Q: Consider the following data on x= height of a building and y = number of stories for nine notable bu...

A: Given data of x= height of building and y = number of stories for nine notable buildings as shown be...

Q: A recent study showed that the modern working person experiences an average of 2.1 hours per day of ...

A: Confidence interval:The (1-α) % confidence interval for population mean µ, when σ is known is given ...

Q: Consider a sample of 54 football games, where 28 of them were won by the home team. Use a 0.05 signi...

A: Test statistic calculation:The probability that the number of home team wins will be greater than on...