Question

suppose lengths of text messages are normally distributed and have a known population standard deviation of 3 characters and an unknown population mean. a random sample of 22 text messages is taken and gives a sample mean of 31 characters. what is the correct interpretation of the 90% confidence interval?

Answer 1

The 90% confidence interval for the lengths of text messages is (26.237, 35.763) characters.

Step-by-step explanation:

The correct interpretation of the 90% confidence interval for the lengths of text messages is that we estimate with 90% confidence that the true population mean length of text messages is between 26.237 and 35.763 characters.

The confidence interval is calculated by taking the sample mean (31 characters) and adding and subtracting the margin of error to it. The margin of error is determined by multiplying the standard deviation (3 characters) by the appropriate z-value for a 90% confidence interval (1.645).

Therefore, the confidence interval formula is: (sample mean - margin of error, sample mean + margin of error) = (31 - 1.645*3, 31 + 1.645*3) = (26.237, 35.763).