Question

# In a test of the effectiveness of garlic for lowering​ cholesterol, 50 subjects were treated with...

As we are not given here that the distribution is normal, but the sample size is greater than 30, therefore we can use the Central limit theorem here to get the distribution of sample mean as a normal distribution.

For n - 1 = 49 degrees of freedom, we get from t distribution tables here:
P( t49 < 1.677 ) = 0.95

Therefore, due to symmetry, we have here:
P( -1.677 < t49 < 1.677) = 0.9

Therefore the confidence interval here is obtained as:

This is the required 90% confidence interval for the population mean here.

As the whole confidence interval lies above 0, therefore we have sufficient evidence here that there is a significant mean net change in LDL cholesterol after the garlic treatment at the 90% confidence that is 10% level of significance.

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