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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