5. A random sample of 15 fence posts from a garden center was found to have a mean length of 1.84 m. The population standard deviation for these posts is taken to be 17cm. (i) Use the t-distribution to find a symmetric 95% confidence interval for the mean length of such posts. (ii) Interpret the 95% confidence interval found in part (i) above. 6. In a survey of 1500 households, it is found that 47% of them have a high-definition television (based on data from the consumer electronics association). Use a 0.01 significance level to test the claim that fewer than half of all households have a high-definition television. Is the result from a few years ago likely to be valid today