Question

Two samples of rats are timed for their maze running time. One group is taking a drug and the other is not. The times are given in the following table:
Rats with drug Rats w/o drug
15 11
12 13
13 9
12 6
10 11
11
Determine whether the use of the test drug results in a different maze running time. Use the .05 level of significance

Answer 1

Question:-

Two samples of rats are timed for their maze running time. One group is taking a drug and the other is not. The times are given in the following table:

Rats with drug Rats w/o drug

15 11

12 13

13 9

12 6

10 11

11

Using z- test statistics Determine whether the use of the test drug results in a different maze running time. Use the .05 level of significance.

Solution :-

The value of z for the given details in the problem is 2.088.

Further Explanation

In doing researches, especially if it's Quantitative Researches, the usage of statistical treatment or tools is very important. Since the statistical tool helps the researcher to achieve one of the research's goals. This is where the Hypothesis Test comes in. Hypothesis Tests is a process of decision making by drawing a conclusion from the population on the basis of the sample size.

Steps In Doing Hypothesis Testing

1. Statement of the Hypotheses

Null HypothesisAlternative Hypothesis

2. Finding the Critical Value

3. Computing the Test Value.

4. The decision to Reject or Accept the Null Hypothesis

5. The implication of the decision in Step 4

One of the Hypothesis Tests that has been employed by the researchers is Z - Test for a Mean. This is used to draw a conclusion from the population on the basis of the sample size. This can be used when the sample size is normally distributed and the standard deviation of the population $\sigma$ is known or given.

The given situation refers to Step 3 of the Hypothesis Testing. The formula that should be used in the given details in the problem is$z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}},$where$\bar{x}$is the sample mean,$\mu$is the population mean,$\sigma$is the population standard deviation, andnis the sample size.

To solve for the value of z, substitute the values of,

$\bar{x}=78.2,\mu=77,\sigma=6$

and n=109into the formula, then simplify the right side using a scientific calculator.

Solution:

$\begin{aligned}z&=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\\z&=\frac{78.2-77}{\frac{6}{\sqrt{109}}}\\z&=\frac{1.2}{\frac{6}{\sqrt{109}}}\\z&=1.2\times{\frac{\sqrt{109}}{6}}\\z&=\frac{1.2\sqrt{109}}{6}\\z&=2.088\end{aligned}$

This clearly shows that the value ofz is 2.088.

Answer 2

z = 2.088

Explanation:

To solve for z we substitute $\bar x = 78.2, \mu = 77, \sigma = 6, n = 109$

in the formula

$z= \frac{\bar x - \mu}{\frac{\sigma}{\sqrt n}}\\\\\implies z = \frac{78.2-77}{\frac{6}{\sqrt109}}\\\\\implies z = 2.088$