Rese careec examining the effects o+ prescheol chld QSeavch Gire, has found that

Question

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Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu = 50 Vs H1 : mu not= 50

where mu is population mean.

Assume alpha = level of significance = 0.05

Here sample size (n) = 10

Here sample data is given and sample size is small so we use one sample t-test.

The test statistic follows t-distribution.

The test statistic is,

t = (Xbar - mu) / (s/sqrt(n))

where Xbar is sample mean.

mu is population mean

s is sample standard deviation

n is sample size

Now we have to find P-value for taking the decision.

95% confidence interval for mu is,

Xbar - E < mu < Xbar + E

where Xbar is sample mean

E is margin of error

E = tc * s/sqrt(n)

where tc is the critical value for t-distribution.

We can test the hypothesis using MINITAB.

steps :

ENTER data into MINITAB sheet --> STAT --> Basic Statistics --> 1-Sample t --> Variables : select data column --> Test mean : 50 --> Options --> Confidence level : 95.0 --> Alternative : not equal --> ok --> ok

One-Sample T: obs

Test of mu = 50 vs mu not = 50

Variable N Mean StDev SE Mean
obs 10 55.50 4.25 1.34

Variable 95.0% CI T P
obs ( 52.46, 58.54) 4.09 0.003

Test statistic = 4.09

P-value= 0.003

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that the population mean is differ than 50.

95% confidence interval for population mean (mu) is (52.46, 58.54)

We are 95% confident that the population mean (mu) lies between 52.46 and 58.54.

And 99% confidence interval for  population mean (mu) is (51.13, 59.87)

We are 99% confident that the population mean (mu) lies between 51.13 and 59.87.

Cohen's d = (Xbar - mu) / s = (55.50 - 50) / 4.25 = 0.26

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