Please show work A researcher collects two independent random samples of sizes n

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Please show work

A researcher collects two independent random samples of sizes n_1 = 28 and n_2 = 33, and computes the means, x bar_1 and x bar_2, and the standard deviations, s_1 and s_2, of each sample. She plans to use a t-test to determine if there is a difference between the two population means, mu_1 and mu_2. She does not know the population standard deviations, nor does she have any reason to believe that they are equal. Using the most conservative approach, calculate how many degrees of freedom, df, are associated with this hypothesis test. Express your answer as an integer.

Explanation / Answer

Here we have given n1= 28 and n2= 33

Here population standard deviation also not known and

She does not believe that population variance are equal.

So degrees of freedom =min{ n1-1, n2-1}

Df =min{ 28-1, 33-1}= min{ 27, 32}= 27

So degrees of freedom = 27

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