Answer:
We conclude that speed is greater than 30 miles per hour.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 30 miles per hour
Sample mean, [tex]\bar{x}[/tex] = 35 miles per hour
Sample size, n = 15
Alpha, α = 0.01
Sample standard deviation, s = 4.7 miles per hour
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 30\text{ miles per hour}\\H_A: \mu > 30\text{ miles per hour}[/tex]
We use one-tailed(right) t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{35 - 30}{\frac{4.7}{\sqrt{15}} } = 4.120[/tex]
Now, [tex]t_{critical} \text{ at 0.01 level of significance, 14 degree of freedom } = 2.624[/tex]
Since,
[tex]t_{stat} > t_{critical}[/tex]
We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis and conclude that speed is greater than 30 miles per hour.
We calculate the p-value.
P-value = 0.00052
Since p value is lower than the significance level, we reject the null hypothesis and accept the alternate hypothesis. We conclude that speed is greater than 30 miles per hour.
