Rouguiatou Diallo - MIDTERM - PART 1 - FALL 2023
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School
CUNY Lehman College *
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Course
703
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
8
Uploaded by ElderFireWalrus24
MIDTERM - PART 1 - FALL 2022
NAME
Exercise # 1 [15pt]
A random sample of 86 eighth-grade students' national mathematics assessment test scores has a mean
score of 287. This test result prompts a state school administrator to declare that the mean score for the
state's eighth graders on this exam is more than 285. Assume that the population standard deviation is
38. At
α
= 0.08, is there enough evidence to support the administration's claim? Use the
Rejection
Region Method [Use CRITICAL VALUES and region to decide NOT the P_VALUE] and your TI 84 /
Technology
to perform this test.
Name of Test
One sample Z test
Conditions
-
The sigma is known = 38
-
Large sample size, n=86
Claim
Claim:
Null Hypothesis (H
₀
): The 8th grade student national mathematics has
amean score of 287
Alternative Hypothesis (H
₁
): The mean score is more than 285.
H0
µ = 285
H1:
µ > 285
Level of significance
α
=
0. 08
1
MIDTERM - PART 1 - FALL 2022
NAME
Test Statistics:
Zstats= 0.488
P-value= 0.3127
Critical Value and
region
Z_=invnorm(0.08)
-1.405
Make a decision
Fail tp reject the null hypothesis because T-stats = -0.488 does not fall
within the rejection region
Interpret Decision
As the p value 0.31 is greater than the level of significance 0.08. There
is insufficient evidence to reject the null hypothesis.
2
MIDTERM - PART 1 - FALL 2022
NAME
Exercise # 2 [15pt]
A car company says that the mean gas mileage for its luxury sedan is at least 21 miles per gallon (mpg).
You believe the claim is incorrect and find that a random sample of 7 cars has a mean gas mileage of 18
mpg and a standard deviation of 4 mpg. At alpha equals
α
=0.025, test the company's claim. Assume the
population is normally distributed. Use the
P-value Method [TECHNOLOGY WORK] – [ Make sure to
fill in both left and right column]
Name of Test
One sample T test
Conditions
Random sample
Population is normally distributed
N is less than 30
State Claim
H0
Ha
The mean gas mileage for its luxury sedan is at least 21 miles
per gallon (mpg)
H0:
21
µ ≥
Ha:
( claim)
µ < 21
Alpha
0.025
3
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MIDTERM - PART 1 - FALL 2022
NAME
Test statistic:
Tstat = -1.98
P-value= 0.047
Rejection Region Method
t_c= invT ( 0.025, 6)
=
−
2. 45
http://www.imathas.com/stattoo
ls/norm.html
Make a decision
Fail to reject the null hypothesis because T-stat= -1.95 does
not fall within the rejection region.
Interpret decision
Based on the P-value Method, there is not enough evidence
to reject the car company's claim that the mean gas mileage
for its luxury sedan is at least 21 mpg at a significance level
of 0.025
4
MIDTERM - PART 1 - FALL 2022
NAME
EXERCISE 3 [15pt]
An energy company wants to choose between two regions in a state to install energy-producing wind
turbines. A researcher claims that the wind speed in Region A is less than in Region B. To test the
regions, the average wind speed is calculated for 60 days in each region. The mean wind speed in
Region A is 13.7 miles per hour. Assume the population standard deviation is 2.7 miles per hour. The
mean wind speed in Region B is 15.2 miles per hour. Assume the population standard deviation is
3.2 miles per hour. At
α
= 0.05, can the company support the researcher's claim?
Use the
Rejection
Region Method.[ Make sure to fill in both left and right columns]
Are the conditions met?
Yes
-Independent and Random samples
-Population standard deviations are known, 2.7mph, 3.2mph
-Normally distributed populations
State the claim
H0
Ha
Claim: The wind speed in Region A is less than in Region B.
H0:
µ1 ≥ µ2
HA:
µ1 < µ2
Level of significance
α = 0. 05
5
MIDTERM - PART 1 - FALL 2022
NAME
Calculate the Standardized Test
Statistic
Z-stat = -2.775
P-value = 0.0028
6
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MIDTERM - PART 1 - FALL 2022
NAME
Identify the Critical values +
Rejection Regions +
Sketch the sampling Distribution
invNorm(0.05)= -1.64
http://www.imathas.com/stattoo
ls/norm.html
Make a decision
Reject the null hypothesis because the p-value is less
than 0.05. This suggest there is enough evidence to
support the researcher claim
7
MIDTERM - PART 1 - FALL 2022
NAME
interpretation
There is enough evidence at the 5% level of
significance to support the researcher's claim that the
wind speed in Region A is less than the wind speed in
Region B.
8