Awashington, d. c., "think tank" announces the typical teenager sent 67 text messages per day in 2017. to update that estimate, you phone a sample of 12 teenagers and ask them how many text messages they sent the previous day. their responses were:

51 175 47 49 44 54 145 203 21 59 42 100

(a) state the decision rule for 0.05 significance level (round to 3 decimal places)
(b) compute the value of the test statistic (round to 3 decimal places)

We reject the null hypothesis and fail to accept it and update that estimate that typical teenager sent does not 67 text messages per day.      

Step-by-step explanation:

We are given the sample:

51, 175, 47, 49, 44, 54, 145, 203, 21, 59, 42, 100

Formula:

where are data points, is the mean and n is the number of observations.  

Sum of squares of differences = 992.25 + 8556.25 + 1260.25 + 1122.25 + 1482.25 + 812.25 + 3906.25 + 14520.25 + 3782.25 + 552.25 + 1640.25 + 306.25 = 3539.363636

We are given the following in the question:  

Population mean, μ =67

Sample mean, = 82.5

Sample size, n = 12

Alpha, α = 0.05

Sample standard deviation, s = 59.5

First, we design the null and the alternate hypothesis

We use One-tailed t test to perform this hypothesis.

b) Formula:

Putting all the values, we have

Now,

a) Since,                

We reject the null hypothesis and fail to accept it and update that estimate that typical teenager send more than 67 text messages per day.

step-by-step explanation: