Analysis of Tyre Lifespans Using Statistical Methods

This report provides a detailed examination of the lifespan of tyres manufactured by two companies: Wheels That Fly! Co. and Loops of Latex Co., using business statistics methods. The analysis involves hypothesis testing to determine if the average lifespan of tyres meets company expectations, comparing tyre lifespans in different environments, and calculating confidence intervals for more precise estimations. Statistical tests such as z-tests (for sample sizes greater than 30) and independent t-tests are employed to test hypotheses about mean differences with significance levels set at 0.05. The results offer insights into the actual lifespan of tyres compared to hypothesized values and investigate potential variations between different usage environments. Additionally, confidence intervals are calculated to provide a range within which the true mean lifespan is expected to lie with 95% certainty.

Running head: BUSINESS STATISTICS
Business statistics
Name of the student
Name of the university
Author’s note

1BUSINESS STATISTICS
Table of Contents
Q1....................................................................................................................................................2
Q2....................................................................................................................................................3
Q3....................................................................................................................................................5

2BUSINESS STATISTICS
Q1.
The company Wheels That Fly! Co. manufactures ‘The Higher Tyre.’ The organization
believes the mean lifespan of tyres is 80,000km. The present analysis investigates the lifespan of
‘The Higher Tyre.’
To test the right tailed test is used.
The z-test is used for the analysis since the sample size if more than 30.
1. Null Hypothesis H0: The mean lifespan of tyres is equal 80,000km
H0 : μ≤ 80000
2. Alternate Hypothesis H A: The mean lifespan of tyres is not equal 80,000km
H A : μ>80000
3. Significance Level : The level of significance is 0.05. Thus, when calculated p-value is
less than 0.05 then we reject the Null Hypothesis, else we accept the Null hypothesis.
Similarly, when the t-critical value is more than the absolute value of t-stat, then we
accept, the Null Hypothesis, else we reject the Null Hypothesis.
4. The t-stat value is -0.9047. Thus, the absolute value of t-stat is 0.9047. The t-crit value
(one-tailed) is 0.5568.
The p-value for the test =0.3663.
5. Since t-crit value (0.5568) is less than absolute t-stat value (0.9047) hence we accept the
Null Hypothesis.
The average, lifespan of tyres is less than 80,000km.
Statistics Value
Count 100
Mean 79850
Standard Deviation 1652.87
Standard Error 165.29
Hypothesized Mean 80000 0.05
tails 2
df 99
t-stat -0.9075
p-value 0.3663
t-crit 0.5568
sig no

3BUSINESS STATISTICS
Q2.
In this question we analyse the lifespan of “Stay Safe tyre” manufactured by Loops of
Latex Co. (LOL). The stay safe tyre model sells well in both outback and cities of Australia.
However, the company suspects that the lifespan of the tyres in Cities is more than that of
Outback. 100 used tyres of from both Outback and Cities was collected. The data was analysed
for the lifespan of the tyres.
To analyse the data two-tailed test is used. The two-tailed test is used since we do not
have the data on the average lifespan of tyres in cities. Thus, initially we assume that the lifespan
of the tyres in both cities and outback are equal. A two-tailed test checks for the possibility of the
relationship in both directions.
To analyse the data the independent sample t-test is used. The independent sample t-test
is used since it compares the lifespan of tyres in outback and cities of Australia. The paired
sample t-test is not used since the tyres used in outback and cities are not related.
Outback Cities
Mean 78769.67 80439.21
Variance 3456197.66 5285115.95
Observations 100 100
Pooled Variance 4370656.80
Hypothesized Mean Difference 0
df 198
t Stat -5.647
P(T<=t) one-tail 0.000
t Critical one-tail 1.653
P(T<=t) two-tail 0.000
t Critical two-tail 1.972
Five-step procedure
1. Null Hypothesis H0 : The lifespan of tyres in Outback and Cities of Australia are equal
H0 : μOutback=μCities
2. Alternate Hypothesis H A : The lifespan of tyres in Outback and Cities of Australia are not
equal
H A : μOutback ≠ μCities
3. Significance Level : The level of significance is 0.05. Thus, when calculated p-value is
less than 0.05 then we reject the Null Hypothesis, else we accept the Null hypothesis.
Similarly, when the t-critical value is more than the absolute value of t-stat, then we
accept, the Null Hypothesis, else we reject the Null Hypothesis.

4BUSINESS STATISTICS
4. The t-stat value is -5.647. Thus, the absolute value of t-stat is 5.647. The t-crit value
(two-tailed) is 1.972.
The p-value for two-tailed test < 0.000.
5. Since, t-crit value is less than absolute t-stat value, hence we reject the Null hypothesis.
Thus, we accept the Alternate hypothesis. Hence, the lifespan of tyres in Outback and
Cities are not equal.
The lifespan of ‘City tyres’ is 80439.21km.
The lifespan of ‘Outback tyres’ is 78769.67km.
Thus, it is seen that the lifespan of ‘City tyres’ is significantly more than ‘Outback tyres.’
The key statistics
Variable 1
(relabel as ‘Outback
tyres’)
Variable 2
(relabel as ‘City tyres’)
Sample mean, x (in km) 78769.67 80439.21
Sample variance, s2 3456197.66 5285115.95
t-stat (refers to our test statistic, the calculated t-
score)
-5.647
Critical t-score (one-tail) 1.653
Critical t-score (two-tail) 1.972

5BUSINESS STATISTICS
Q3.
The 95% confidence interval can be calculated as follows:
The mean lifespan of all car tyres in Manly is 78270 km.
The standard deviation of the lifespan of car tyres is 2719.17km
Thus the standard error of the lifespan = 271.92
Thus, the margin of error = 532.96
Statistics Value
Average 78270
Standard Deviation 2719.17
Count 100
Standard Error 271.92
z-value 1.96
Margin of Error 532.96
Lower Margin 77737
Upper Margin 78803
Hence, the lower and upper limit of the 95% confidence interval for the lifespan of car
tyres at Manly is 77737, 78803 km.
Thus, it can be interpreted that when another survey is conducted for the lifespan of car
tyres at Manly, then there is a 95% chance that the average lifespan of the car tyres would lie
between 77737 and 78803km.