STA101 Business Statistics- Statistical Concepts
Create an executive summary report of 1,000 words or less (four pages or less) that addresses an issue within the business environment using the following statistical concepts:
- Hypothesis testing I (involving taking a sample from one population)
- Hypothesis testing II (involving taking a sample each from two populations)
- Confidence intervals (stating the population mean within a range of numbers).
Answer:
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.
- Null Hypothesis : The mean lifespan of tyres is equal 80,000
km
- Alternate Hypothesis : The mean lifespan of tyres is not equal 80,000km
- 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.
- 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.
- 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 |
|
a |
0.05 |
|
tails |
2 |
|
df |
99 |
|
t-stat |
-0.9075 |
|
p-value |
0.3663 |
|
t-crit |
0.5568 |
|
sig |
no |
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 |
|
Mean |
78769.67 |
|
Variance |
3456197.66 |
|
Observations |
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
- Null Hypothesis The lifespan of tyres in Outback and Cities of Australia are equal
- Alternate Hypothesis The lifespan of tyres in Outback and Cities of Australia are not equal
- 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.
- 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.
- 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, (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 | |
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.
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