Question

1.) A recent survey showed that high school girls average 110 text messages daily. The population standard deviation is 25 text messages. 1 In repeated samples of size n = 64 high school girls, the expected value of the sample mean is, a 1.719 b 10.488 c 13.75 d 110 2.) In repeated samples of size n = 64 high school girls, the standard error of the sample mean is, a 25 b 5 c 3.125 d 0.391 3.) In repeated samples of size n = 64 high school girls, the fraction of sample means that fall within ±5 messages from the population mean is, a 0.8904 b 0.9260 c 0.9538 d 0.9824 4.) The margin of error for the middle interval which includes 95% of means from samples of size n = 64 is, a 5.763 b 5.941 c 6.125 d 6.248

Answer 1

Here we have

Sample size: n=64

The sampling distribution of sample mean will be approximately normal distribution with mean

and standard deviation is

(1)

Correct option d: 110

(2)

Correct option c: 3.125

(3)

The z-score for is

The z-score for is

Using z table, the fraction of sample means that fall within ±5 messages from the population mean is

Correct option (a) 0.8904

(d)

The z-scores -1.96 and 1.96 has 0.95 area between them. The margin of error for middle 95% of means from samples of size n = 64 is

Correct option (c) 6.125