Test of hypotheses: difference between means and proportions

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1. SafeRoad Stores is redesigning the checkout lanes in its stores throughout the country. Two designs have been suggested. Tests on customer checkout times have been conducted at two stores where the two new systems have been installed. A summary of the sample data follows:

System A System B
Sample size = 25 Sample size = 25
Sample mean checking out time = 4.3 minutes Sample mean checkout time = 3.3 minutes
Sample standard deviation = 2.0 minutes Sample standard deviation = 3.0 minutes

At the 0.05 significance level, perform a statistical test to see the two systems are significantly different.

Small Sample Size (Independent Sample)

Data
Sample 1: System A
Mean of sample 1= M 1 = 4.3 minutes
Standard deviation of sample 1= s1 = 2.0 minutes
Sample size of sample 1= n1 = 25

Sample 2: System B
Mean of sample 2= M 2 = 3.3 minutes
Standard deviation of sample 2= s2 = 3.0 minutes
Sample size of sample 2= n2 = 25
Hypothesized difference between means = 0
Significance level= 0.05

1) Hypothesis
Null Hypothesis: Ho: M 1 = M 2 (M 1 is equal to M 2)
Alternative Hypothesis: H1: M 1 not equal to M 2 :( M 1 is not equal to M 2 )
No of tails= 2 (Both tails )
This is a 2 tailed (Both tails ) test because we are testing that M 1 not equal to M 2
Significance level=alpha (a) = 0.05 or 5%

2) Decision rule
we use t distribution as we are dealing with small sample sizes
t at the 0.05 level of significance and 48 degrees of freedom (=n1+n2-2) and 2 tailed test= 2.0106
t critical = ± 2.0106

if sample statistic is <-2.0106 or > 2.0106, Reject Null Hypothesis, else Accept Null Hypothesis
Alternatively
if p value is less than the significance level (= 0.05 ), Reject Null Hypothesis, else Accept Null Hypothesis

3) Calculation of sample statistics
Sample 1: Sample 2:
System A System B
Mean =M = 4.30 3.30
Standard deviation =s= 2.00 3.00
Sample size=n= 25 25

Difference ...