New York University Hypothesis Testing and MINITAB Data File Questions

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nagubavr1234

Mathematics

New York University

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1 question need to use minitab. You need to have the access to minitap.

Questions are attached below.

1.Use MINITAB data file is posted

The data in Used cars data file indicate the prices of 95 used BMW cars. Some have four-wheel drive (the model identified by the Xi type and the others two-wheel drive (the model denoted by the letter I). If we treat data as sample of the typical selling prices of these models, what do you conclude? Do four-wheel drive models command a higher price as two wheel drive, or not?

Use α = 0.1.

2.The accompanying table shows the golf scores of nine golfers before and after a lesson given by a golf professional. Using α=0.01 determine if the average score is lower for the golfers after the golf lesson when compared with before the golf lesson.



3.The following table shows the results of two random samples that measured the average number of minutes per charge for AA Lithium-ion (Li-ion) rechargeable batteries versus Nickel-Metal Hydride (NiMH) rechargeable batteries. Complete parts a through c.

Li-ion

NiMH

Sample mean

96.3

82.9

Sample standard deviation

6.7

11.5

Sample size

14

18

a.Using α=0.05 determine if the average number of minutes per charge differs between these two battery types.

b.Find a 90% confidence interval to estimate the difference between the average number per charge differs between these two battery types.



4.A study was recently conducted at a major university to determine whether there is a difference in the proportion of business school graduates who go on to graduate school within five years after graduation and the proportion of non-business school graduates who attend graduate school. A random sample of 400 business school graduates showed that 70 had gone to graduate school while, in a random sample of 500 non-business graduates, 128 had gone on to graduate school.

a.Based on these sample data, and a 0.08 level of significance, conduct an appropriate test statistic?

b.What is the p-value for the test you have conducted in part “a”.

Unformatted Attachment Preview

Price $31,995.00 $25,995.00 $21,995.00 $25,995.00 $24,995.00 $26,995.00 $28,995.00 $28,995.00 $28,995.00 $35,495.00 $29,900.00 $28,900.00 $25,900.00 $28,900.00 $28,900.00 $26,900.00 $28,900.00 $25,900.00 $28,995.00 $27,995.00 $32,900.00 $27,900.00 $25,900.00 $24,900.00 $27,900.00 $26,400.00 $25,900.00 $25,200.00 $26,100.00 $24,900.00 $28,900.00 $28,900.00 $28,900.00 $27,400.00 $29,900.00 $33,600.00 $29,400.00 $32,900.00 $33,600.00 $35,900.00 $31,495.00 $26,995.00 $28,995.00 $24,495.00 $26,495.00 $31,795.00 Type i i i i i xi xi i i i i i i xi xi xi xi i xi xi xi i i i i i i i i i xi xi xi xi i xi xi xi xi xi i i i xi xi xi Year 2005 2002 2001 2002 2002 2002 2002 2002 2002 2004 2002 2002 2002 2003 2002 2003 2002 2002 2003 2002 2003 2003 2002 2002 2003 2002 2002 2002 2002 2002 2003 2003 2003 2002 2002 2002 2002 2002 2004 2004 2006 2003 2003 2002 2003 2003 $41,495.00 $34,995.00 $39,495.00 $31,995.00 $28,900.00 $20,900.00 $24,900.00 $26,900.00 $24,900.00 $26,900.00 $27,900.00 $27,900.00 $26,900.00 $26,900.00 $32,900.00 $30,900.00 $28,989.00 $29,989.00 $28,989.00 $28,989.00 $31,989.00 $30,898.00 $31,989.00 $29,989.00 $29,989.00 $33,989.00 $39,989.00 $24,989.00 $24,989.00 $35,989.00 $35,989.00 $31,989.00 $35,989.00 $33,989.00 $31,989.00 $26,985.00 $22,985.00 $25,875.00 $24,875.00 $25,875.00 $26,985.00 $28,985.00 $31,985.00 $29,985.00 $33,985.00 $29,985.00 $29,985.00 i i i xi i i i i i i i i xi xi i xi i i i i i xi xi xi xi xi i i i i xi xi xi xi xi i i i i i i i i i i xi xi 2006 2004 2006 2003 2003 2001 2002 2003 2002 2002 2003 2003 2002 2003 2004 2002 2003 2003 2003 2003 2004 2002 2003 2003 2002 2004 2006 2001 2003 2004 2005 2003 2003 2002 2002 2002 2001 2002 2002 2002 2002 2004 2004 2004 2004 2002 2002 $28,985.00 xi $27,895.00 xi 2003 2002
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Explanation & Answer

Hi again! 👋 I only got less than 2 hours left for this question, so I'll be uploading the answers now. Once you've read this message, please share with me the data for item #2 so I can work on it right away. Thank you!

1. Use MINITAB data file is posted
The data in Used cars data file indicate the prices of 95 used BMW cars. Some have four-wheel
drive (the model identified by the Xi type and the others two-wheel drive (the model denoted by
the letter I). If we treat data as sample of the typical selling prices of these models, what do you
conclude? Do four-wheel drive models command a higher price as two wheel drive, or not?
Use α = 0.1.

Solution:
A two-sample t-test was performed to determine if there is a difference between the mean selling
prices of two-wheel and four-wheel drive models. This test method was used because the
population standard deviations are not given.
Using the given excel file as input, the following results were obtained from MINITAB.

Figure 1. Results of two-sample t-test between the mean selling prices of two-wheel and fourwheel drive models (confidence level = 90%, significance level = 0.10).

From the results, we find that the t-value = -2.42, df = 92, and p-value = 0.009. Since the p-value
is less than 𝛼=0.10, we reject the null hypothesis. Thus, the difference between the mean selling
prices of the two models is statistically significant. Specifically, the mean selling price of fourwheel drive models is estimated to be $1,756 higher than two-wheel models. One can be 90%
confident that the difference between the two population means is at least $818.

2.The accompanying table shows the golf scores of nine golfers before and after a lesson given by
a golf professional. Using α=0.01 determine if the average score is lower for the golfers after the
golf lesson when compared with before the golf lesson.

------------------------NO DATA GIVEN------------------------

3. The following table shows the results of two random samples that measured the average number
of minutes per charge for AA Lithium-ion (Li-ion) rechargeable batteries versus Nickel-Metal
Hydride (NiMH) rechargeable batteries. Complete parts a through c.
Li-ion

NiMH

Sample mean

96.3

82.9

Sample standard deviation

6.7

11.5

Sample size

14

18

a. Using α=0.05 determine if the average number of minutes per charge differs between these two
battery types.

Solution:
For this problem, let us denote 𝜇1 as the average number of minutes per charge for Li-ion batteries
and 𝜇2 as the average number of minutes per charge for NiMH batteries. The null and alternate
hypotheses are as follows:
Null hypothesis: There is no difference between the average number of minutes per charge
between Li-ion and NiMH batteries.
H0: 𝜇1 − 𝜇2 = 0
Alternate hypothesis: There is a difference between the average number of minutes per charge...


Anonymous
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