You are a famous and successful statistical consultant because of your amazing t
ID: 3359388 • Letter: Y
Question
You are a famous and successful statistical consultant because of your amazing training in EDPS 459. Spotify, the music streaming company, enlists your services to determine if they are wasting their money marketing their streaming service to college students. Specifically, they want to know if college students listen to Spotify less than other Spotify users. If so, they will spend their marketing dollars on another demographic. They provide you with the following information: The average Spotify user listens to Spotify for 148 minutes, on average, every day (µ = 148). You randomly sample 3 college students from the population of undergraduates in the United States, and record how many minutes they listen to Spotify each day. These students’ data are provided below. Student Number of Minutes 1 160 2 180 3 200 Mean Minutes 180 You decide to implement a 2-tailed test (i.e., non-directional hypotheses) to answer Spotify’s question, as it is more conventional and more conservative than a 1-tailed test. State your null and alternative hypotheses in words and mathematical symbols. What is the most appropriate statistical test to answer this research question and test these hypotheses? Why can’t we use a different test? Do these data meet the assumptions of the chosen statistical test? Explain how it meets or does not meet each assumption. Test these hypotheses at an alpha level of 0.05 ( = 0.05). Report the values of any tests you calculate, and any critical values that you use.
Explanation / Answer
State your null and alternative hypotheses in words and mathematical symbols.
The average Spotify user listens to Spotify for 148 minutes, on average, every day Ho: =148
The average Spotify user listens to Spotify is diffrent from 148 minuetes, H1: !=148
What is the most appropriate statistical test to answer this research question and test these hypotheses?
we use T test , as we conisder a smaller size an the sample distribution is approximately normal
Why can’t we use a different test? Do these data meet the assumptions of the chosen statistical test?
We don't have the population standard deviation data provided
Test these hypotheses at an alpha level of 0.05 ( = 0.05). Report the values of any tests you calculate, and any critical values that you use.
Given that,
population mean(u)=148
sample mean, x =180
standard deviation, s =20
number (n)=3
null, Ho: =148
alternate, H1: !=148
level of significance, = 0.05
from standard normal table, two tailed t /2 =4.303
since our test is two-tailed
reject Ho, if to < -4.303 OR if to > 4.303
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =180-148/(20/sqrt(3))
to =2.7713
| to | =2.7713
critical value
the value of |t | with n-1 = 2 d.f is 4.303
we got |to| =2.7713 & | t | =4.303
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 2.7713 ) = 0.1093
hence value of p0.05 < 0.1093,here we do not reject Ho
ANSWERS
---------------
null, Ho: =148
alternate, H1: !=148
test statistic: 2.7713
critical value: -4.303 , 4.303
decision: do not reject Ho
p-value: 0.1093
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