Question

In: Statistics and Probability

A new species of bird, the Lilac-Breasted Raven, was recently discovered. A researcher is attempting to...

A new species of bird, the Lilac-Breasted Raven, was recently discovered. A researcher is attempting to determine the average incubation time for this species' eggs to hatch. For compatison, the eggs of a common raven have eggs that take an average of μ = 19 days to hatch with a standard deviation of σ = 1.23 days. A sample of 13 eggs was collected and incubated. The length of time (in days) is listed in the table below:

17 19 22

21 17 16

18 18 16

19 17 20

18

At the 5% significance level, perform and interpret a hypothesis test to determine if the average incubation time for the Lilac-Breasted Raven is less than 19 days. (You may assume that the hatch times are normally distributed, and that σ = 1.23 days.)

Expert Solution

As per the provided information:

The researcher wants to test whether the average incubation time for the Lilac-Breasted Raven is less than 19 days.

The total number of eggs, n is 13.

The population mean, is 19 days.

The population standard deviation, is 1.23 days.

The significance level, is 0.05.

The given data set of incubated eggs is given by,

17, 19, 22, 21, 17, 16, 18, 18, 16, 19, 17, 20, 18

The sample mean can be calculated as:

The null and the alternative hypothesis can be stated as:

The test is left tailed.

As the sigma value is known, so the appropriate test statistic to be used is z- test statistic.

Test statistic:

Hence, the value of the z-statistic is -2.02.

Decision of the test using critical value:

At the significance level 0.05, the left tailed critical value obtained from z-table is -1.645.

Since, the test statistic (-2.02) is less than the critical value (-1.645), so the decision is to reject the null hypothesis.

Decision of the test using p- value:

Using the standard normal table, the obtained p-value is given by,

Since, the p-value (0.0217) is less than the level of significance (0.05), so the decision is to reject the null hypothesis.

In conclusion, there is enough evidence to support that the average incubation time for the Lilac-Breasted Raven is less than 19 days at the significance level 0.05.

orchestra answered 2 years ago

A new species of Plasmodium was recently discovered from a patient and the National Institutes of...

A new species of Plasmodium was recently discovered from a patient and the National Institutes of Health has hired you to investigate. Describe how infection with this microorganism is likely to be detected, a potential strategy to prevent infection and the disease likely to be associated with this pathogen

Suppose a hypothetical bird species (species Gamma) differs from a closely related bird species (species Delta)...

Suppose a hypothetical bird species (species Gamma) differs from a closely related bird species (species Delta) in several ways, including being much more aggressive. How would you set up an experiment to determine if environment or genetics plays a larger role in the Gamma bird species aggression? You would relocate some adult Gamma birds to a Delta bird habitat and some adult Delta birds to a Gamma habitat and compare the aggressive behaviors in their new environment to their aggressive...

A new species of microorganism is discovered in a barren desert habitat. Researchers find that the...

A new species of microorganism is discovered in a barren desert habitat. Researchers find that the species does not require any from of water to exist. How would discovery of this species require modification of hypotheses about the origins of life on earth? a. The idea of membrane-bound protobionts as the first cells would not necessarily be true any longer. b. The presence of an electronic charge between water and lightning in Earth's early atmosphere would be modified. c. Amino...

A species of butterfly found in Central America (Macrosoma heliconiaria) recently has been discovered to have...

A species of butterfly found in Central America (Macrosoma heliconiaria) recently has been discovered to have ultrasound-detecting ears just in front of its forewings (a slightly different location than the ears found in Noctuid moths). Unlike other butterflies, this species is nocturnal. A) Using the correct terminology, briefly explain why this discovery of ears in an unrelated species is considered to be evidence that the ears in these butterflies and in Noctuid moths are anti-predator adaptations. B) Design a simple...

A new archaebacterium species was discovered that strives at elevated temperatures. List three differences in the...

A new archaebacterium species was discovered that strives at elevated temperatures. List three differences in the membrane composition of the archaebacterium: 1 2 3 If the archaebacterium is normally grown at 80oC is transferred to medium at 37oC, give two changes (adaptations) the bacterium can make to the composition of membrane lipids. Be specific and include modifiers such as increase/decrease, etc. 1 2

You have discovered a new species of platypus with an unprecedented 7 layer cortex, with an...

You have discovered a new species of platypus with an unprecedented 7 layer cortex, with an additional neuronal layer compared to the typical 6 layers mammalian cortex. Propose an experiment to determine in what sequence the neuron layers were generated during brain development in this platypus. This question has been written based on the following article: " The determination of neuronal fate in the cerebral cortex", Review article by Susan K. McConnell

You have discovered a new species of insect while hiking around the BioReserve! Based on the...

You have discovered a new species of insect while hiking around the BioReserve! Based on the fruit fly and other insects, you know that larvae have patches of cells known as “imaginal discs,” each of which will contribute to an appendage of the adult (e.g. antenna, wing, or leg). Moreover, you know that the decapentaplegic(dpp) gene is expressed in the imaginal discs that contribute to the wings, but not in those that contribute to the antennae or legs. For each...

You have discovered a new species of sea squirt and you have named it Seasquirtus laker...

You have discovered a new species of sea squirt and you have named it Seasquirtus laker after your alma mater. Sea squirts feed by sucking water through a tube into the pharynx, and then into the stomach. This water not only contains nutrition, but also potential toxins and microbes from the environment. As an immunologist, you are curious about how S. laker protects itself from environmental threats. What are 3 different mechanisms that S. laker might prevent microbial infection or...

_18. In bird and mammal species, females are more _ and males are more __. A....

_____18. In bird and mammal species, females are more ___________ and males are more ________. A. K – selected, R - selected B. R – selected, K - selected _____19. Mating behavior would be described as __________ while social mating behavior is be described as___________. A. behavior leading up to and including copulation; behavior lasting after copulation, until their young are raised and sometimes beyond B. behavior during mate attraction; behavior during copulation C. shaped only by natural selection; shaped only...

A bird species in danger of extinction has a population that is decreasing exponentially (A =...

A bird species in danger of extinction has a population that is decreasing exponentially (A = A0ekt). Five years ago, the population was at 1400 and today only 1000 of the birds are alive. Once the population drops below 100, he situation will be irreversible. When will this happen? According to the U. S. Bureau of the Census, in 2000 there were 35.3 million residents of Hispanic origin living in the United States. By 2010, the number had increased to...