Please show steps Previously, an organization reported that teenagers spent 4.5
ID: 3127457 • Letter: P
Question
Please show steps Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are: a. Ho: x ¯ = 4.5, Ha : x ¯ > 4.5 b. Ho: 4.5, Ha: < 4.5 c. Ho: = 4.75, Ha: > 4.75 d. Ho: = 4.5, Ha: > 4.5
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u = 4.5
Ha: u > 4.5 [ANSWER, OPTION D]
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As we can see, this is a right tailed test.
df = n - 1 = 14
Getting the test statistic, as
X = sample mean = 4.75
uo = hypothesized mean = 4.5
n = sample size = 15
s = standard deviation = 2
Thus, t = (X - uo) * sqrt(n) / s = 0.484122918
Also, the p value is
p = 0.317892101
As P is large, we FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant evidence that the true mean is greater than 4.5 hours at 0.05 level.