hypothesis testing�unknown variance, large sample size
Attempt the question before watching the video on the next slide.
The packaging on an electric light bulb states that the average length of life of bulbs is 1000 hours. A consumer association thinks that this is an overestimate and tests a random sample of 64 bulbs, recording the life x hours, of each bulb.
Σx = 63 910.4 Σx2 = 63 824 061
Is there evidence, at the 10% significance level, that the statement on the packaging is overestimating the length of life of this type of light bulb?
Attempt the question before watching the video on the next slide.
A random sample of 75 eleven year olds performed a simple task and the time taken, t minutes, noted for each. The results were summarised as follows:
Σt = 1215 Σt2 = 21 708
Test, at the 1% level, whether there is evidence that the mean time to perform the task is greater than 15 minutes.
| n | Σx | Σx2 | | hypotheses | Level of significance |
1 | 65 | 6500 | 650 842.4 | | H0: µ = 99.2 H1: µ ≠ 99.2 | 5% |
2 | 65 | 6500 | 650 842. 4 | | H0: µ = 99.2 H1: µ > 99.2 | 5% |
3 | 80 | 6824 | | 2508.8 | H0: µ = 86.2 H1: µ < 86.2 | 10% |
4 | 100 | 685 | 4728.25 | | H0: µ = 7 H1: µ ≠ 7 | 1% |