APFIVE Conclusion of a One-Sample T-Test
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 |
A
Reject the alternative hypothesis; the true mean is less than or equal to $$6.5$$ kW.
B
Reject the null hypothesis; there is sufficient evidence that the true mean exceeds $$6.5$$ kW.
C
Fail to reject the null hypothesis; there is insufficient evidence to conclude that the true mean exceeds $$6.5$$ kW.
D
The test is inconclusive because the sample size is too small.
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