Statistics Problem

Question

Following are prices of a random sample of 18 smart TVs sold at a particular department store with screen sizes between 46’’ and 50’’. Find the 90% confidence interval for the true mean price of a smart TV purchased at this store. Assume the prices are normally distributed.

448 498 597 599 649 699 529 749 628 950 798 369 498 669 499 599 355 469

Answer 1

Since we do not know the population standard deviation and the sample size is < 30, we will use the critical t value in the computation of the confidence interval:

Confidence Interval = sample mean +/- critical t * standard error

For a sample size of 18 and confidence level 90% we will use the critical t corresponding to a tail probability of 0.05 and 17 degrees of freedom (sample size - 1).

Standard error will be equal to the computed sample standard deviation divided by the square root of the sample size.

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