As production manager for Samsonite Luggage, you are concerned about the breakin
ID: 3156555 • Letter: A
Question
As production manager for Samsonite Luggage, you are concerned about the breaking strength of your company's suitcases so that when people sit on them to close them or when they're thrown around at airports, they stay in one piece. You assume that the breaking strength of all the suitcases is normal, and hire a team of dedicated apes to jump on 25 pieces of luggage to find that the sample mean breaking strength is 61.3 lbs and the sample standard deviation is 2.5 lbs. Construct a 95% and 99% confidence interval for the true mean breaking strength of all suitcases. Before carrying out this testing, you asked the previous production manager for a value for the true mean breaking strength of all suitcases, and the manager said 60 lbs. You think that current luggage is more durable (i.e., the true mean breaking strength is larger now). State the appropriate hypotheses and conduct the appropriate tests at alpha =.05 and alpha =.01 Had you thought that the true mean breaking strength of all suitcases is different than 60 lbs, state the appropriate hypotheses and conduct the appropriate tests at alpha =.05 and alpha =.01.Explanation / Answer
Solution:
Here, we are given,
Sample size = n = 25
Sample mean = xbar = 61.3
Sample standard deviation = SD = 2.5
Part a
The confidence interval formula is given as below:
Confidence interval
Lower limit = sample mean – t*SD/sqrt(n)
Upper limit = sample mean + t*SD/sqrt(n)
The 95% confidence interval is given as below:
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
2.5
Sample Mean
61.3
Sample Size
25
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.5
Degrees of Freedom
24
t Value
2.0639
Interval Half Width
1.0319
Confidence Interval
Interval Lower Limit
60.27
Interval Upper Limit
62.33
The 99% confidence interval is given as below:
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
2.5
Sample Mean
61.3
Sample Size
25
Confidence Level
99%
Intermediate Calculations
Standard Error of the Mean
0.5
Degrees of Freedom
24
t Value
2.7969
Interval Half Width
1.3985
Confidence Interval
Interval Lower Limit
59.90
Interval Upper Limit
62.70
Part b
Here, we have to use the one sample t test for the population mean. The null and alternative hypothesis is given as below:
H0: µ = 60 versus Ha: µ > 60
The test statistic formula is given as below:
Test statistic = t = (xbar - µ) / [SD/sqrt(n)]
The test at 0.05 level of significance is given as below:
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
60
Level of Significance
0.05
Sample Size
25
Sample Mean
61.3
Sample Standard Deviation
2.5
Intermediate Calculations
Standard Error of the Mean
0.5000
Degrees of Freedom
24
t Test Statistic
2.6000
Upper-Tail Test
Upper Critical Value
1.7109
p-Value
0.0079
Reject the null hypothesis
The test at 0.01 level of significance is given as below:
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
60
Level of Significance
0.01
Sample Size
25
Sample Mean
61.3
Sample Standard Deviation
2.5
Intermediate Calculations
Standard Error of the Mean
0.5000
Degrees of Freedom
24
t Test Statistic
2.6000
Upper-Tail Test
Upper Critical Value
2.4922
p-Value
0.0079
Reject the null hypothesis
Part c
Yes, there is a sufficient evidence to say that mean breaking strength of all suitcases is different than 60 lbs at 5% significance level and there is no sufficient evidence to say that mean breaking strength of all suitcases is different than 60 lbs at 1% significance level.
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
60
Level of Significance
0.05
Sample Size
25
Sample Mean
61.3
Sample Standard Deviation
2.5
Intermediate Calculations
Standard Error of the Mean
0.5000
Degrees of Freedom
24
t Test Statistic
2.6000
Two-Tail Test
Lower Critical Value
-2.0639
Upper Critical Value
2.0639
p-Value
0.0157
Reject the null hypothesis
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
60
Level of Significance
0.01
Sample Size
25
Sample Mean
61.3
Sample Standard Deviation
2.5
Intermediate Calculations
Standard Error of the Mean
0.5000
Degrees of Freedom
24
t Test Statistic
2.6000
Two-Tail Test
Lower Critical Value
-2.7969
Upper Critical Value
2.7969
p-Value
0.0157
Do not reject the null hypothesis
Yes, there is a sufficient evidence to say that mean breaking strength of all suitcases is different than 60 lbs at 5% significance level and there is no sufficient evidence to say that mean breaking strength of all suitcases is different than 60 lbs at 1% significance level.
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
2.5
Sample Mean
61.3
Sample Size
25
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.5
Degrees of Freedom
24
t Value
2.0639
Interval Half Width
1.0319
Confidence Interval
Interval Lower Limit
60.27
Interval Upper Limit
62.33
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