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 ztest 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 pvalue is less than 0.05 then we reject the Null Hypothesis, else we accept the Null hypothesis.
Similarly, when the tcritical value is more than the absolute value of tstat, then we accept, the Null Hypothesis, else we reject the Null Hypothesis.
 The tstat value is 0.9047. Thus, the absolute value of tstat is 0.9047. The tcrit value (onetailed) is 0.5568.
The pvalue for the test =0.3663.
 Since tcrit value (0.5568) is less than absolute tstat 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 
tstat 
0.9075 
pvalue 
0.3663 
tcrit 
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 twotailed test is used. The twotailed 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 twotailed test checks for the possibility of the relationship in both directions.
To analyse the data the independent sample ttest is used. The independent sample ttest is used since it compares the lifespan of tyres in outback and cities of Australia. The paired sample ttest 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) onetail 
0.000 
t Critical onetail 
1.653 
P(T<=t) twotail 
0.000 
t Critical twotail 
1.972 
Fivestep 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 pvalue is less than 0.05 then we reject the Null Hypothesis, else we accept the Null hypothesis.
Similarly, when the tcritical value is more than the absolute value of tstat, then we accept, the Null Hypothesis, else we reject the Null Hypothesis.
 The tstat value is 5.647. Thus, the absolute value of tstat is 5.647. The tcrit value (twotailed) is 1.972.
The pvalue for twotailed test < 0.000.
 Since, tcrit value is less than absolute tstat 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, s^{2}^{} 
3456197.66 
5285115.95 
tstat (refers to our test statistic, the calculated tscore) 
5.647 

Critical tscore (onetail) 
1.653 

Critical tscore (twotail) 
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 
zvalue 
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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