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# Two Sample test of hypotheses

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27. A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. The information is summarized below

Statistic Men Women
Sample mean 24.51 22.69
Population standard deviation 4.48 3.86
Sample size 35 40

At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? What is the p-value?

46. Grand Strand Family Medical Center is specifically set up to treat minor medical emergencies for visitors to the Myrtle Beach area. There are two facilities, one in the Little River Area and the other in Murrells Inlet. The Quality Assurance Department wishes to compare the mean waiting time for patients at the two locations. Samples of the waiting
times, reported in minutes, follow:
Assume the population standard deviations are not the same. At the .05 significance level, is there a difference in the mean waiting time?

Location Waiting Time
Little River 31.73 28.77 29.53 22.08 29.47 18.60 32.94 25.18 29.82 26.49
Murrells Inlet 22.93 23.92 26.92 27.20 26.44 25.62 30.61 29.44 23.09 23.10 26.69 22.31

https://brainmass.com/statistics/hypothesis-testing/two-sample-test-of-hypotheses-259851

#### Solution Preview

"27. A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. The information is summarized below

Statistic Men Women
Sample mean 24.51 22.69
Population standard deviation 4.48 3.86
Sample size 35 40

At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? What is the p-value?
"

This is a case of test of hypothesis for Large Sample Sizes

Data

Sample 1: Men
Mean of sample 1= M1 = 24.51
Standard deviation of sample 1= s1 = 4.48
Sample size of sample 1= n1 = 35

Sample 2: Women
Mean of sample 2= M2 = 22.69
Standard deviation of sample 2= s2 = 3.86
Sample size of sample 2= n2 = 40

Hypothesized difference between means = 0
Significance level= 0.01

1) Hypothesis
Null Hypothesis: Ho: M 1 = M 2 (M 1 is equal to M 2)
Alternative Hypothesis: H1: M 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 not equal to M 2
Significance level=alpha (a) = 0.01 or 1%

2) Decision rule
we use z distribution as we are dealing with large sample sizes
Z at the 0.01 level of significance 2 tailed test = 2.5758
z critical = ± 2.5758

if sample statistic is <-2.5758 or > 2.5758, Reject Null Hypothesis, else Accept Null Hypothesis
Alternatively
if p value is less than the significance level (= 0.01 ), Reject Null Hypothesis, else Accept Null Hypothesis

3) Calculation of sample statistics

Sample 1: Sample 2:
Men Women
Mean =M = 24.51 22.69
Standard deviation =s= 4.48 3.86
Sample size=n= 35 40

Difference of means= 1.82 =24.51 - 22.69

Standard error of difference of mean =s x1-x2 =square root of (s1 2 /n1+s2 2/n2)=
=square root of ( ...

#### Solution Summary

Tests the hypotheses for differences between means.

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