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

Question

3 months ago

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A Washington, 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)

Mathematics

1 answer:

PIT_PIT [12.4K] · Answer 1 · 2026-02-22T14:35:11+03:00

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:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ represents the data points, $\bar{x}$ denotes the mean, and n indicates the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{990}{12} = 82.5$

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

$S.D = \sqrt{\frac{3539.363636}{11}} = 59.5$