Of the statistics above the one that would be appropriate fo

Of the statistics above, the one that would be appropriate for testing the hypothesis that the true mean () is less than 0if X is normally-distributed and the variance is estimated from which sample?

2:

Of the statistics above, the one that would be appropriate for testing the hypothesis that the true mean () is less than 0if the distribution of X is unknown and the sample size is 35 is?

Solution

1.

X is normally distrbuted, so we can use z. [So, we are down to just A or B]

Now, as we just estimate the variance, we do not have sigma, just s. Thus,

OPTION B: z = (X - uo)/(s/sqrt(n)) [ANSWER]

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2)

If the distribution of X is unknown, we should use t.

Thus,

OPTION C: t = (X - uo)/(s/sqrt(n)) [ANSWER]

Note: If in your class, you use z for n > 30, then please choose option B.