A Washington, D.C., "think tank" announces the typical teenager sent 67 text messages per day in 2017. To update that estimate,
1 answer:
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.
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Answer:
1. x=±4
2. t=±9
3. r=±10
4. x=±12
5. s=±5
Step-by-step explanation:
1. x^2 = 16
By extracting the square root on both sides
x=±4
2. t^2=81
Again, take the square root of each side
t=±9
3. r^2-100=0
r=±10
4. x²-144=0
We rewrite as x²=144
Applying square roots
x=±12
5. 2s²=50
s=±5 ..
This problem can be addressed by applying the normal approximation to a binomial distribution.
Calculations:
Mean (μ) = np = 10,000 × 0.5 = 5,000
The standard deviation (σ) is given by:
The probability of obtaining more than 5,100 tails is 0.0228, whereas the probability of fewer than 5,100 tails is 0.9772.
Thus, the odds of having more than 5,100 tails are:
0.0228 : 0.9772 = 1 : 42.86.
Calculations:
Mean (μ) = np = 10,000 × 0.5 = 5,000
The standard deviation (σ) is given by:
The probability of obtaining more than 5,100 tails is 0.0228, whereas the probability of fewer than 5,100 tails is 0.9772.
Thus, the odds of having more than 5,100 tails are:
0.0228 : 0.9772 = 1 : 42.86.