Answer:
No, at alpha equals 0.10, we do not have enough evidence to support the county's claim.
Step-by-step explanation:
We are given that a county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 miles per hour.
A random sample of 15 vehicles has a mean speed of 31 miles per hour and a standard deviation of 4.7 miles per hour.
<em><u>Let </u></em><em><u> = true mean speed of the vehicles.</u></em>
SO, <u>Null Hypothesis</u>, :
30 miles per hour {means that the mean speed of vehicles is lesser than or equal to 30 miles per hour}
<u>Alternate Hypothesis,</u> :
> 30 miles per hour {means that the mean speed of vehicles is greater than 30 miles per hour}
The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean speed of 15 vehicles = 31 mph
s = sample standard deviation = 4.7 mph
n = sample of vehicles = 15
So, <em><u>test statistics</u></em> = ~
= 0.824
<u><em>Hence, the value of test statistics is 0.824.</em></u>
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<em>Now at 0.10 significance level, the t table gives critical value of 1.345 at 14 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 0.824 < 1.345, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.</em>
<em />
Therefore, we conclude that the mean speed of vehicles is lesser than or equal to 30 miles per hour which means that the county's claim is not supported.
