APFIVE Conclusion of a One-Sample T-Test
A manufacturer claims that its new air-conditioning unit uses $$6.5$$ kilowatts per day. A consumer agency collects a random sample (data shown in the table) and conducts a one-sample t-test. At the 5% significance level, what conclusion should be drawn regarding the claim that the true mean usage exceeds $$6.5$$ kW?
TABLE:
| Sample Size (n) | Sample Mean ($$\bar{x}$$ in kW) | Sample Standard Deviation (s in kW) |
|---|---|---|
| 50 | 7.0 | 1.4 |
A
The test is inconclusive because the sample size is too small.
B
Fail to reject the null hypothesis; there is insufficient evidence to conclude that the true mean exceeds $$6.5$$ kW.
C
Reject the null hypothesis; there is sufficient evidence that the true mean exceeds $$6.5$$ kW.
D
Reject the alternative hypothesis; the true mean is less than or equal to $$6.5$$ kW.
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