A Washington, D.C., "think tank" announces the typical teenager sent 67 text messages per day in 2017. To update that estimate,

Answer:

We reject the null hypothesis, leading us to revise the estimate that a typical teenager sends 67 text messages each day.

Step-by-step explanation:

The sample provided is:

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

Formula:

where represents the data points, denotes the mean, and n indicates the number of observations.

The sum of squares of differences equals 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

The following information is provided 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

Initially, we formulate the null and alternate hypothesis

We apply the One-tailed t test for this hypothesis testing.

b) Formula:

Substituting all the values gives us

Now,

a) As such,

We discard the null hypothesis and adjust the estimate, concluding that teenagers send more than 67 text messages daily.