Answer:
Exact Form:
3 /14
Decimal Form:
_____
0.2 142857
Step-by-step explanation:
Tim Worker expects Social Security benefits of $937 per month. His wife, Mary, is eligible for a wife's benefit of 50 percent of
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Answer:
Step-by-step explanation:
Given
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Find x
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Collect like terms
Divide by 300
Answer:
We conclude that the average training time for government-employed security personnel is lesser than or equal to those employed by private security companies.
Step-by-step explanation:
We are given that a random sample of 12 government-employed security personnel, average training time was 72 hours, with a sample standard deviation of 8 hours. In a random sample of 16 privately employed security personnel, training time was 65.4 hours, with a sample standard deviation of 12.3 hours.
We have to conduct a hypothesis test to determine that average training time for government-employed security personnel is higher than those employed by private security companies.
<em>Let </em><em> = mean training time for the population of airport security personnel employed by the federal government.</em>
<em /><em> = mean training time for the population of airport security personnel employed by private security companies.</em>
SO, Null Hypothesis, :
or
{means that the average training time for government-employed security personnel is lesser than or equal to those employed by private security companies}
Alternate Hypothesis, :
or
{means that the average training time for government-employed security personnel is higher than those employed by private security companies}
The test statistics that will be used here is <u>Two-sample t test statistics</u> as we don't know about the population standard deviations;
T.S. = ~
where, = sample average training time of government-employed security personnel = 72 hours
= sample average training time of privately employed security personnel = 65.4 hours
= sample standard deviation of government-employed security personnel = 8 hours
= sample standard deviation of privately employed security personnel = 12.3 hours
= sample of government-employed security personnel = 12
= sample of privately employed security personnel = 16
Also, =
= 10.694
So, <em><u>test statistics</u></em> = ~
= 1.616
<em>Since, in the question we are not given with the level of significance at which hypothesis can be tested, so we assume it to be 5%. Now at 5% significance level, the t table gives critical value of 1.706 at 26 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 1.616 < 1.706, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.</em>
Therefore, we conclude that the average training time for government-employed security personnel is lesser than or equal to those employed by private security companies.