The Willow Run Outlet Mall has two Haggar Outlet Stores, one located on Peach Street and the other on Plum Street. The two stores are laid out differently, but both store managers claim their layout maximizes the amounts customers will purchase on impulse. A sample of 10 customers at the Peach Street store revealed they spent the following amounts more than planned: $17.58, $19.73, $12.61, $17.79, $16.22, $15.82, $15.40, $15.86, $11.82, $15.85. A sample of 14 customers at the Plum Street store revealed they spent the following amounts more than they planned when they entered the store: $18.19, $20.22, $17.38, $17.96, $23.92, $15.87, $16.47, $15.96, $16.79, $16.74, $21.40, $20.57, $19.79, $14.83. For data analysis, a t test: two-sample assuming unequal variances was used. Hypothesis Test: Independent Groups (t test, unequal variance) Peach Street Plum Street 15.8680 18.2921 mean 2.3306 2.5527 std. dev. 10 14 n 20 df -2.42414 difference (Peach Street - Plum Street) 1.00431 standard error of difference 0 hypothesized difference -2.41 t .0255 p-value (two-tailed) -5.28173 confidence interval 99.% lower 0.43345 confidence interval 99.% upper 2.85759 margin of error At the .01 significance level, is there a difference in the mean amount purchased on an impulse at the two stores? Explain these results to a person who knows about the t test for a single sample but who is unfamiliar with the t test for independent means
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
- The Willow Run Outlet Mall has two Haggar Outlet Stores, one located on Peach Street and the other on Plum Street. The two stores are laid out differently, but both store managers claim their layout maximizes the amounts customers will purchase on impulse. A sample of 10 customers at the Peach Street store revealed they spent the following amounts more than planned: $17.58, $19.73, $12.61, $17.79, $16.22, $15.82, $15.40, $15.86, $11.82, $15.85. A sample of 14 customers at the Plum Street store revealed they spent the following amounts more than they planned when they entered the store: $18.19, $20.22, $17.38, $17.96, $23.92, $15.87, $16.47, $15.96, $16.79, $16.74, $21.40, $20.57, $19.79, $14.83. For data analysis, a t test: two-sample assuming unequal variances was used.
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Hypothesis Test: Independent Groups (t test, unequal variance) |
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Peach Street |
Plum Street |
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15.8680 |
18.2921 |
mean |
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2.3306 |
2.5527 |
std. dev. |
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10 |
14 |
n |
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20 |
df |
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-2.42414 |
difference (Peach Street - Plum Street) |
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1.00431 |
standard error of difference |
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0 |
hypothesized difference |
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-2.41 |
t |
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.0255 |
p-value (two-tailed) |
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-5.28173 |
confidence interval 99.% lower |
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|
0.43345 |
confidence interval 99.% upper |
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|
2.85759 |
margin of error |
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At the .01 significance level, is there a difference in the mean amount purchased on an impulse at the two stores? Explain these results to a person who knows about the t test for a single sample but who is unfamiliar with the t test for independent means.
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