In this equation, x = 7.
In order to solve this you are going to need to use logarithmic functions. By taking a logarithm you can eliminate exponents.
First we're going to take the logarithm of both sides, which allows us to put the exponents in front of the terms.
(x + 2)Log5 = 9Log5
Now that we've done this, we can divide both sides by Log5 and eliminate that term.
x + 2 = 9
From here, we simply need to subtract in order to solve.
x = 7
Answer:
The null hypothesis will not be rejected.
Step-by-step explanation:
The hypothesis for the test is:
<em>H</em>₀: There is no difference between the two population means, i.e. <em>d</em> = 0.
<em>Hₐ</em>: There is a significant difference between the two population means, i.e. <em>d</em> ≠ 0.
Consider the Excel output attached.
The mean of the differences is, .
The standard deviation of the differences is, .
Compute the test statistic as follows:
The degrees of freedom is, n - 1 = 7.
Compute the <em>p</em>-value as follows:
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
<em>p</em>-value = 0.112 > α = 0.02.
The null hypothesis will not be rejected.