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QNT 561 Week 5 Individual Assignment - Inferential Statistics and Findings - A+ Guide!

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RUNNING HEAD: INFERENTIAL STATISTICS 1
QNT/561 Week 5
Assignment
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Date
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RUNNING HEAD: INFERENTIAL STATISTICS 2
Inferential Statistics
The research question is to understand whether the satisfaction of the customer with
his/her initial product affects his/her preference to buy from the same store. In this study, the
dependent variable is the amount of purchases of each customer, while the independent variable
is the satisfaction of the customer with his/her first product (either <5 or >5). 400 people are
studied, of which 200 are people who were satisfied with the initial product while the other 200
are people who were not satisfied with the initial product.
To establish the fact whether the two means are different, a two-sample t-test assuming
unequal variances is being applied. The null and alternative hypotheses are:
𝐻
π‘œ
: πœ‡
1
= πœ‡
2
(The population mean of sales in group 1 is equal to the population mean of sales in
group 2)
𝐻
π‘Ž
: πœ‡
1
β‰  πœ‡
2
(The population mean of sales in group 1 is not equal to the population mean of
sales in group 2)
Below is the two-sample t-test from the data analysis plugin in Microsoft Excel Β©.
T-test: Two-sample assuming unequal variances
t-Test: Two-Sample Assuming Unequal Variances
Group 1
Sales
Group 2
Sales
Mean
421.91
222.295
Variance
38466.84613
17206.10852
Observations
200
200
Hypothesized Mean
Difference
0
df
347
t Stat
11.96426533

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RUNNING HEAD: INFERENTIAL STATISTICS 3
P(T<=t) one-tail
3.7222E-28
t Critical one-tail
1.649256711
P(T<=t) two-tail
7.4444E-28
t Critical two-tail
1.966824003
The two-sample t-test above shows a t-statistic of 11.964, with an accompanying p-value
of 7.444E-28 (approximately zero). The p-value is much smaller than the significance level of
0.05, so the null hypothesis is rejected; the significance level can be anywhere from 0.01 to 0.10,
and the null hypothesis would still be rejected. Therefore, there is a very small chance that the
rejection of the null hypothesis is a Type I or Type II error.
There is sufficient evidence to suggest that the two population means are not equal.
Therefore, people who are satisfied with the initial product tend to spend more than people who
are dissatisfied with the initial product.

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