Question

# A researcher wishes to test the following hypotheses: H 0 : μ ≤ 10 H A...

A researcher wishes to test the following hypotheses: H 0 : μ ≤ 10 H A : μ > 10 Based on 54 independent observations, he calculates a sample mean of 11 and a sample standard deviation of 4. Calculate the T-score he should use for his test statistic. Report your answer to at least three decimal places, e.g., 0.123.

Solution :

A researcher wishes to test the following hypotheses: H0 : μ ≤ 10 vs HA : μ > 10 based on 54 independent observations, he calculates a sample mean of 11 and a sample standard deviation of 4, we have to calculate the T-score that he should use for his test statistic.

The appropriate hypothesis is given as,

The appropriate test statistic is given as,

From the data given , we have the following information :

Thus , the value of the test statistic is given as ,

Thus, the T - score that the researcher should use for his test statistic is = 1.837 ................ (Ans)

_________________________

#### Earn Coins

Coins can be redeemed for fabulous gifts.