Question 9 options: 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. Is there enough evidence to support the claim using a level of significance of 1%?

If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is not significantly lower than 18.7 months

Step-by-step explanation:

Data given and notation  

represent the sample mean

represent the sample standard deviation for the sample  

sample size  

represent the value that we want to test

represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is lower than 18.7, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

 (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

P-value

The first step is calculate the degrees of freedom, on this case:  

Since is a one side test the p value would be:  

Conclusion  

If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is not significantly lower than 18.7 months

the circle one