A random survey of 75 death row inmates revealed that the mean length of time on

Question

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.2 years with a standard deviation of 6.7 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years.

Part (a)

Is this a test of one mean or proportion?

test of one mean

test of proportions    

Part (b)

State the null and alternative hypotheses.

H0: 15
Ha: < 15H0: 15
Ha: > 15    H0: 15
Ha: = 15H0: = 15
Ha: 15H0: = 15
Ha: > 15

Part (c)

Is this a right-tailed, left-tailed, or two-tailed test?

right-tailed testleft-tailed test    two-tailed test

Part (d)

What symbol represents the random variable for this test?

X    n

Part (e)

In words, define the random variable for this test.

the number of inmates on death rowthe proportion of time spent on death row for 75 inmates    

the standard deviation of time spent on death row for 75 inmates

the amount of time spent on death row for 75 inmates

the mean time spent on death row for 75 inmates

Part (f)

Is the population standard deviation known?

Yes

No    

If so, what is it? (Enter your answer to one decimal place. If the standard deviation is not known enter DNE.)

Part (g)

Calculate the following.

(i) Enter your answer to one decimal place.
x =  

(ii) Enter your answer to one decimal place.
s =  

(iii) Enter your answer as a whole number.
n =

Part (h)

Which test should be used?

Student's t-testNormal test    

Part (i)

State the distribution to use for the hypothesis test. (Enter your answer in the form z or tdf where df is the degrees of freedom.)

Part (j)

Find the p-value. (Round your answer to four decimal places.)

Part (k)

At a pre-conceived

= 0.05,

what do you determine for each of the following?(i) Decision:

reject the null hypothesisdo not reject the null hypothesis    

(ii) Reason for the decision:

Since > p-value, we reject the null hypothesis.Since < p-value, we reject the null hypothesis.    Since > p-value, we do not reject the null hypothesis.Since < p-value, we do not reject the null hypothesis.

(iii) Conclusion (write out in a complete sentence):

There is sufficient evidence to conclude that the mean length of time on death row is not 15 years.

There is not sufficient evidence to conclude that the mean length of time on death row is not 15 years.   

Explanation / Answer

a)test of one mean

b)Ha: 15H0: = 15

Part (c) two-tailed test

Part (d)X

Part (e)the mean time spent on death row for 75 inmates

Part (f) No

DNE

g)x=17.2

s = 6.7

astd error of mean =std deviation/(n)1/2=0.7736

n=75

h)Student's t-test

i) tdistribution df=74

j)test stat t=(X-mean)/std error =(17.2-15)/0.7736=2.8437

p value =0.0029

k)reject the null hypothesis

lo)There is sufficient evidence to conclude that the mean length of time on death row is not 15 years.

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