Question 1. For the given data, (a) find the test statistic, (b) find the standardized
test statistic, (c) decide whether the standardized test statistic is in the rejection
region, and (d) decide whether you should reject or fail to reject the null hypothesis.
The samples are random and independent.
Claim: µ 1= µ2, n = 0.05.
Sample statistics: x1= 15, s1= 0.9, n 1= 50 and x2 = 13, s2 = 1.5, n2= 60
Ho = µ 1= µ2
Ha = µ 1≠ µ2
a)The test statistic is =x1 - x2 = 15 - 13 = 2
b)The standardized test statistic is ______(Round to two decimal places as needed.)
You can use s1 and s2 instead of σ1 and σ2
σ x1- x2 =sqrt {(0.92/50 )+(1.52/60)} = sqrt(0.0537)=0.2317
z = (15-13) - 0/0.2317 =8.63
c)Is the standardized test statistic in the rejection region?
Yes the standardized test statistic is in the rejection region as 8.63 is greater than
zcritical=1.96 for α=0.05(confidence interval=95%)
d)Should you reject or fail to reject the null hypothesis?
As the standardized test statistic falls in the rejection region ,we reject the null
hypothesis.
Final Statement: At 5% significance level, there is enough evidence to conclude that
there is a significant difference in the mean differences of the two samples taken
Ho: µ1= µ2; H :µ1*µ2.._-I - - -'=""IHo. At the 5% significance level, there is I_-. - - """Ievidence to reject the claim
Question 2. A safety engineer records the braking distances of two types of tires.
Each randomly selected sample has 35 tires. The results of the tests are shown in
the figure. At α = 0.10, can the engineer support the claim that the mean braking
distance is different for the two types of tires? Assume the samples are randomly
selected and that the samples are independent. Complete parts (a) through (e).
Type A: x1 = 41 feet s1 = 4.9 feet n1=35
Type B: x2=45 feet, s2=4.7 feet n2=35
a)Identify the claim and state Ho and H,. What is the claim?
Ho :µ1= µ2
The mean braking distance is the same for the two types of tires.
Ha: µ 1≠ µ2(claim)
The mean braking distance is different for the two types of tires.
Useful tip or rule of thumb: no matter what ,the null hypothesis always contains
the equality.
b)Find the critical value(s) and identify the rejection region(s).
At α = 0.10,
The critical value(s) is/are z critical = + 1.645 , - 1.645 (Round to three decimal
places as needed. Use a comma to separate answers as needed.)
c)Find the standardized test statistic z= (41-45) - 0/sqrt{(4.92/35)+(4.72/35)}
z=-4/1.14767= - 3.485
d)Decide whether to reject or fail to reject the null hypothesis. Choose the correct
answer below:
Zstandard test statistic = -3.485 does lies in the rejection region as there it does not
fall in the range of critical values of +1.645<z<-1.645 ;
hence we reject the null hypothesis
Reject H0• The standardized test statistic falls in the rejection region.
e)Interpret the decision in the context of the original claim.
At the 10% significance level, there is I_ _,=.
the mean braking distance for Type A tires isI
"Ievidence to C==:GJ the claim that
IType D tires.
Question 3. The mean exam score for 48 male high school students is 24.5 and the
standard deviation is 4.8.The mean exam score for 57 female high school students is
21.5 and the standard deviation is 4.2. At a= 0.01, can you reject the claim that male
and female high school students have equal exam scores?
Answer the below:
Identify the claim and state Ho and H,. What is the claim?Male high school students
have greater exam scores than female students? Male and female high school
students have different exam scores.? Male and female high school students have
equal exam score? Male high school students have lower exam scores than female
students?
a)What are Ho and H?
Ho :µ1= µ2 (claim)
The mean exam score is the same for the male and female students.
Ha: µ 1≠ µ2
The mean exam score is not the same for the male and female students.
b)The critical value(s) at is/are ___________?
At α = 0.10,
The critical value(s) is/are z critical = + 1.645 , - 1.645
c)Find the standardized test statistic z=__________ (Round to three decimal places as
needed.
σ x1- x2 =sqrt {(4.82/48 )+(4.22/57)} =sqrt(0.7895)=0.8885
z=(24.5 - 21.5 )- 0/0.8885 = 3.376
d)Decide whether to reject or fail to reject the null hypothesis. Choose the correct
answer below:
.Reject H0• The standardized test statistic is not in the rejection region.
Fail to reject H0• The standardized test statistic is not in the rejection region.
correct :Reject H0• The standardized test statistic is in the rejection region.
Fail to reject H0• The standardized test statistic is in the rejection region.
e)Interpret the decision in the context of the original claim.
At the 10% significance level, there is ___not enough_______evidence to
___support_________the claim that male high school students have exam
scores_____equal to___female high school students' exam scores.
Question 4. Is the difference between the mean annual salaries of statisticians in
Region I and Region2 more than $7000? To decide, you select a random sample of
statisticians from each region. The results of each survey are below. At a= 0.10, what
should you conclude?
Region 1:x1=1$68,000 s1=$8755, n1=43 Region 2:X2=$65,000,s2=$9075, n2 =41
a)Identify the null and alternate hypothesis and state it mathematically_________
Ho: µ1- µ2 ≤7000
Ha: µ1- µ2>7000
Determine the critical value(s).
zcritical= _____________?(Round to two decimal places as needed. Use a comma to
separate answers as needed.)
Calculate the standardized test statistic.z= ___________(Round to two decimal places as
needed.)
Choose the correct answer below.
Reject H0• At the 1% significance level, there is sufficient evidence to support the
claim that the difference between the mean annual salaries is more than S7000.
Reject H0• At the 1% significance level, there is insufficient evidence to support the
claim that the difference between the mean annual salaries is more than S7000.
Fail to reject H0• At the 1% significance level, there is insufficient evidence to
support the claim that the difference between the mean annual salaries is more than
S7000.
Fail to reject H0• At the 1% significance level, there is sufficient evidence to support
the claim that the difference between the mean annual salaries is more than S7000.
needs correction:1% or 10 %
Question 5.Use the t-distribution table to find the critical value(s) for the indicated
alternative hypotheses, level of significance a, and sample sizes n 1and n2. Assume
that the samples are independent, normal, and random.
what are the indicated alternative hypothesis…I have all other formulae ready,just
want the values
Find the critical value(s) assuming that the population variances are equal.
(type aninteger or decimal rounded to three decimal places as needed. Use a comma
to separate answers as needed.) ___________?
Find 'the critical value(s) assuming that the population variances are not equal.
(type aninteger or decimal rounded to three decimal places as needed. Use a comma
to separate answers as needed.)____________?
Question 6. Find the answers using the following information:
Ho: µ,_xxxx_(let me know what is the sign here)_ µ2, a= 0.05Sample statistics: x 1=
2213, s1= 162, n 1= 14
x2 = 2325, s2 = 38, n2 = 13
Assume T is 1.782
Find the test statistic. ____________?(type an integer or decimal rounded to three
decimal places as needed.)
Decide whether the standardized test statistic is in the rejection region. The
standardized test statistic, t, is _________the rejection region.
Decide whether you should reject or fail to reject the null hypothesis.
____________the null hypothesis.
Question 7. A personnel director in a particular state claims that the mean annual
income is greater in one of the state's counties (county A) than it is in another
county (county D). In County A, a random sample of 17 residents has a mean annual
income of $41,000 and a standard deviation of $8400.In County B, a random sample
of8 residents has a mean annual income of $38,800 and a standard deviation of
$5800. At a = 0.05, answer parts (a) through (e). Assume the population variances
are not equal.
a)Identify the claim and state Ho and Ha
Ho: µ1≤µ2
Ha: µ1>µ2 (claim)
Ho: The mean annual income of A is less than or equal to B
Ha: The mean annual income of A is greater than B
b)State Ho and Ha mathematically_____________?
Ho: µ1≤µ2
Ha: µ1>µ2 (claim)
c)What is the correct claim below?
The mean annual incomes in counties A and D are equal.
The mean annual incomes in counties A and D are not equal.
The mean annual income in county A is less than in county D.
The mean annual income in county A is greater than in county B.
What are Ho and H,__________?
The null hypothesis, H0, ________·The alternative hypothesis, Ha is__________?
The null hypothesis, H0, is ___________?The alternative hypothesis, Ha ___________?
Already written..
Which hypothesis is the claim?The alternative hypothesis or the Null
Hypothesis_______? Alternative hypothesis is the claim
Question 8. Construct a 90% confidence interval (α =1-0.9 = 0.1) for µ1- µ2 with the
sample statistics for mean cholesterol content of a hamburger from two fast food
chains. Assume the populations are approximately normal with unequal variances.
x1= 128 mg, s1= 3.87 mg, n 1= 17
x2 = 62 mg, s2 = 2.06 mg, n2 =16
At α =0.1, t critical=1.697
µ1-µ2=x1 -x2 + t critical * σ x1- x2
=128-62 + 1.697*
Enter the endpoints of the interval. ________<µ1-µ2 <__________(Round to the nearest
integer as needed.)