Conclusion of a One-Sample T-Test

Question

A manufacturer claims that its new air-conditioning units use a mean of $6.5$ kilowatts (kW) per day. To investigate if the true mean usage exceeds this amount, a consumer agency conducts a one-sample t-test using data from a random sample, as shown in the table. At a significance level of $α = 0.05$ , what is the correct conclusion?

TABLE:

Sample Size (n)	Sample Mean ( $\bar{x}$ in kW)	Sample Standard Deviation (s in kW)
50	7.0	1.4

TABLE:
| Sample Size (n) | Sample Mean ($$\bar{x}$$ in kW) | Sample Standard Deviation (s in kW) |
|-----------------|------------------------------|------------------------------------|
| 50              | 7.0                          | 1.4                                |

Accepted Answer

Reject the null hypothesis; there is sufficient evidence that the true mean exceeds $$6.5$$ kW.

Answer

The test is inconclusive because the sample size is too small.

Answer

Reject the alternative hypothesis; the true mean is less than or equal to $$6.5$$ kW.

Answer

Fail to reject the null hypothesis; there is insufficient evidence to conclude that the true mean exceeds $$6.5$$ kW.

Conclusion of a One-Sample T-Test

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