SOLUTION: Question 3 Many people believe that the average number of Facebook friends is 338. The population standard deviation is 43.2. A random sample of 50 high school students in a count

Question 1183829: Question 3
Many people believe that the average number of Facebook friends is 338. The population standard deviation is 43.2. A random sample of 50 high school students in a country revealed that the average number of Facebook friends was 350. At α = 0.05,
a. Why was the sample collected?
b. Calculate the significant level for this hypothesis test.
c. Find the critical value for this test at α = 0.05.
d. Calculate the test value.
e. Based on the test value and the critical value is there enough evidence to conclude that the mean number of friends is greater than 338?
f. Determine whether it is a one - tail or a two - tail test.
g. Find the maximum error E for estimating population mean.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
a. The sample was collected to determine whether the belief that the average number of Facebook friends of 338 is still true.

b. The signicance level is , no need to calculate. (But do you know what this value means?)

c. By the CLT, the sampling distribution of the sample means is approximately normally distributed with mean , and standard dev .
===> critical value for a ONE-TAILED test (will explain later why) is 1.645.

d.

e. By comparing the test value with the critical z, we reject the null hypothesis, and conclude that
there is evidence that the average number of Facebook friends may have increased from 338.

f. It is a one-tailed test because the sample value of 350 is quite far from 338 (on the high side), enough to suspect that the
true sample mean may have increased from 338.

g. Maximum error is given by

Done.
RELATED QUESTIONS
Many people believe that the average number of Facebook friends is 338. The population... (answered by Theo)

Suppose the number of friends a randomly chosen Facebook member has is normally... (answered by stanbon)

1.The mean number of close friends for the population of people living in the Philippines (answered by Boreal)

SHOW THE COMPLETE SOLUTION AND THE SIX STEPS IN SOLVING THIS HYPOTHESIS TESTING The... (answered by Theo)

A researcher revealed that the average number of people who have a driver's license out... (answered by Boreal)

1.We wish to estimate what percent of 18 to 25-year old's that own a Samsung phone. Out... (answered by math_tutor2020)

Can someone show me how to solve these problem below using the Central Limit Theorem?... (answered by rothauserc)

If a population has a standard deviation of 16, what is the minimum number of samples... (answered by ewatrrr)

You want to obtain a sample to estimate how much parents spend on their kids birthday... (answered by Boreal)