Do mice show a preference for using one paw over the other? Attempting to answer this question, a researcher tested a random sample of 48 mice and observed which forepaw (right or left) the mice used to retrieve food from a narrow tube. Eighteen of the mice used their right paw, while the rest used their left paw.
Does this data suggest that mice show a preference towards one paw over the other? Carry out the appropriate test and include all steps for full credit.
During the course of the experiment, the researcher noticed that individual mice sometimes switched which forepaw they used to retrieve the food. So she repeated this study on the same 48 mice, but measured each one 10 times and she recorded which forepaw was used each time. With her new dataset of 480 observations, would you be able to run the same analysis as in part (a)? If so, carry out the analysis and compare the results. If not, why not?

Answer:

It all depends on the food they are going for, just like humans, mice have instincts. For example, if you were falling forward, which foot would you put out? Most likely the opposite one. I hope this helps you!

Step-by-step explanation:

Using hypotheses testing,

In both cases, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that mice show a preference towards one paw over the other.

We have,

(a)

To test whether the data suggest that mice show a preference towards one paw over the other, we can use a one-sample proportion test.

The null hypothesis (H0) is that the proportion of mice that use their right paw is 0.5 (indicating no preference towards one paw over the other).

The alternative hypothesis (Ha) is that the proportion of mice that use their right paw is different from 0.5 (indicating a preference towards one paw over the other).

We can use a significance level (alpha) of 0.05.

To conduct the test, we can calculate the test statistic using the formula:

z = (p - 0.5) / √(0.5 x 0.5 / n)

where p is the proportion of mice that use their right paw, and n is the sample size.

Using the given data, we have:

p = 18/48 = 0.375

n = 48

Plugging in the values, we get:

z = (0.375 - 0.5) / √(0.5 x 0.5 / 48) = -1.714

Using a standard normal distribution table or calculator,

We can find the p-value associated with this test statistic.

The p-value is the probability of observing a test statistic as extreme as -1.714 or more extreme, assuming the null hypothesis is true.

The p-value for this test is 0.0869.

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.

This means that we do not have sufficient evidence to conclude that mice show a preference towards one paw over the other, based on the given sample.

(b)

With the new dataset of 480 observations, we can still conduct a similar analysis using a one-sample proportion test.

However, since each mouse was measured 10 times, the observations are no longer independent.

Therefore, we need to use a different test that accounts for the dependency between observations, such as McNemar's test.

McNemar's test is a test of the marginal homogeneity of a two-way table, where the same subjects are measured twice on a binary outcome.

In this case, we can create a 2x2 contingency table of the number of times each mouse used their right or left paw, and conduct a McNemar's test on this table.

The null hypothesis for McNemar's test is that there is no difference in the proportions of mice that use their right or left paws.

The alternative hypothesis is that there is a difference.

To conduct the test, we can calculate the test statistic using the formula:

chi-squared = (|b-c|-1)² / (b+c)

where b is the number of mice that used their right paw more often, and c is the number of mice that used their left paw more often.

Using the given data, we have:

b = 214

c = 244

Plugging in the values, we get:

chi-squared = (|214-244|-1)² / (214 + 244) = 2.417

Using a chi-squared distribution table or calculator with 1 degree of freedom (since we have a 2x2 table), we can find the p-value associated with this test statistic.

The p-value is the probability of observing a test statistic as extreme as 2.417 or more extreme, assuming the null hypothesis is true.

The p-value for this test is 0.119.

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.

This means that we do not have sufficient evidence to conclude that there is a difference in the proportions of mice that use their right or left paws, based on the new dataset.

Thus,

In both cases, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that mice show a preference towards one paw over the other.

Learn more about the hypotheses test here:

https://brainly.com/question/28331914

#SPJ2

A box of donuts cost $9. You want to send donuts to the local nursing home. Set up an equation to find how many boxes you can send if you have $72.

Jill wants to paint the front and top surfaces of each step leading to her porch. There are 6 steps like the one shown. How many total square inches of the steps will she paint?

A: 1,296

B: 1,776

C: 3,552

D: 5,760​

4. Are the expressions 3(y + 1) and 3y + 3, equivalent for y = 1? y= 2? y 3?​

A walking path 78 mile long Colleen planted 14 bushes the same distance apart along the path how far power are the 1st 2 bushes along the path​

BRAINLIEST!!! find the probability for numbers 11 and 13 please

(please answer if you know) On a​ map, 1 inch equals 5.2 miles. Two houses are 3.5 inches apart on the map. What is the actual distance between the​ houses? Use pencil and paper. Show how you can represent the scale with two different ratios. What ratio is more helpful for solving the​ problem? Explain.

At a school carnival, 51 out of 68 tickets sold were early-admission tickets. What percentage of the tickets were early-admission tickets?

The length of one rectangle is 3 1/2 mm with a width of 2 4/5 mm . What is the area of the rectangle?

Find the distance between the points (4.5,-1.5), (4.5,7.25)
The distance is ____.

-7x + 2y = -5
y = -7x + 8
explain how please

Pricilla makes a profit of $24.50 on every scarf she sells the materials for each scarf cost
$8.39 how much does Priscilla sell each scarf for?

85% of x is 51. Write an equation that represents the situation.

The area of a rectangle with a
length of 10 cm and a width of 3
cm.

if 40% percent is a number of 35 what is 50% of that number

what is the slope of 4x-3y=18

I will give Brainliest answer!

What is the volume of the cylinder below? write your answer in terms of pie.

Height= 11.5 cm
Radius= 6 cm

Anyone who know what the answer please please?!

guys someon about to comit u know what so go to this link and help out
https://brainly.com/question/22760250

PLEASE HELP !! ILL GIVE BRAINLIEST !! 100 POINTS

please help i have been stuck on this for 3 hours

Select the most accurate statement regarding the normal distribution. Group of answer choices It is always the appropriate distribution in simulation modeling. It does not permit negative values. There is a 95% chance that values will be within ±2 standard deviations of the mean. The user must specify the maximum positive value allowed. It is obtained by the positive and negative square roots of a uniform random variable.

The sales rate is 8%. If Janelle buys a gymnastics mat priced at $87 , how much tax will she pay?

PLs help me. I need to find the measure of B

⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️HELP HELP HELP HELP - A triangle has side lengths of 7, 23, and 25. Is the triangle a right triangle? *
Yes, the triangle is a right triangle.
No, the triangle is not a right triangle.
There is not enough information to tell if the triangle is a right triangle.

Hey guys, I just got braces and they are really uncomfy so how long did it take yall to get used to them?

A class consists of 1/2 freshmen, 1/8 sophomores, and 1/8 juniors; the rest are seniors. What fraction of the class is seniors?

WILL MARK BRAINLY FOR WHO EVER GETS THIS RIGHT

There are 400 thousand people living in Miami and 300 thousand people living in Anchorage. Which statement below shows which city has more people living in it? - 400 thousand people > 300 thousand people, so there are more people living in Miami. 400 thousand people < 300 thousand people, so there are more people living in Miami. 400 thousand people > 300 thousand people, so there are more people living in Anchorage. 400 thousand people < 300 thousand people, so there are more people living in Anchorage.​

PLEASE HELPP!!!!

Please find the areas of these shape

Pleaseee helppp me on this