Answer:
a. No, there is not enough evidence to support the claim using a level of significance of 1%.
b. Null Hypothesis, :
18.7 months
c. Alternate Hypothesis<u>,</u> :
< 18.7 months
d. P-value of hypothesis test = 0.0199 or 1.99%
e. We conclude that the convicted burglars spend more than or equal to 18.7 months in jail, on average.
Step-by-step explanation:
We are given that a researcher wants to check the claim that convicted burglars spend less than 18.7 months in jail, on average.
She takes a random sample of 67 such cases from court files and finds that the mean is 16.8 months with a standard deviation of 7.3 months.
<em><u>Let </u></em><em><u> = true mean time convicted burglars spend in jail.</u></em>
SO, <u>Null Hypothesis</u>, :
18.7 months {means that the convicted burglars spend more than or equal to 18.7 months in jail, on average}
<u>Alternate Hypothesis,</u> :
< 18.7 months {means that the convicted burglars spend less than 18.7 months in jail, on average}
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 time spent in jail = 16.8 months
s = sample standard deviation = 7.3 months
n = sample of cases = 67
So, <em><u>test statistics</u></em> = ~
= -2.13
Hence, the value of test statistics is -2.13.
<u>Now, P-value of the test statistics is given by;</u>
P-value = P( < -2.13) = 0.0199 or 1.99%
- If the P-value of test statistics is more than the level of significance, then we will not reject our null hypothesis as it will not fall in the rejection region.
- If the P-value of test statistics is less than the level of significance, then we will reject our null hypothesis as it will fall in the rejection region.
<em>Now, here the P-value is 0.0199 or 1.99% which is clearly higher than the level of significance of 1%, so we will not reject our null hypothesis as it will not fall in the rejection region.</em>
Therefore, we conclude that the convicted burglars spend more than or equal to 18.7 months in jail, on average.