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:

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