A radio station states that 30% of the songs they play each week are from Canadian artists. A DJ working at the station claims that the actual percentage differs from what the station states. The DJ takes a random sample of 87 songs played during a given week and finds that 28 of them are from Canadian artists. Use this information to answer the questions below.
A radio station states that 30% of the songs they play each week are from Canadian artists. A DJ working at the station claims that the actual percentage differs from what the station states. The DJ takes a random sample of 87 songs played during a given week and finds that 28 of them are from Canadian artists. Use this information to answer the questions below.
a. Suppose the DJ wishes to perform a hypothesis test of his claim. Select the most appropriate null and alternative hypotheses for this hypothesis test.
- H0:p^≠0.3Ha:p^=0.3
- H0:x―=0.3Ha:x―≠0.3
- H0:μ≠0.3Ha:μ=0.3
- H0:p=0.3Ha:p≠0.3
- H0:μ=0.3Ha:μ≠0.3
- H0:p≠0.3Ha:p=0.3
- H0:p^=0.3Ha:p^≠0.3
- H0:x―≠0.3Ha:x―=0.3
b. To assess his hypothesis, the DJ wants to compute a bootstrap-based confidence interval from his sample. Which of the following uses of the quantile()
- c(quantile(B$mean, 0.04), quantile(B$mean, 0.96))
- c(quantile(B$mean, 0.02), quantile(B$mean, 0.96))
- c(quantile(B$mean, 0.01), quantile(B$mean, 0.99))
- c(quantile(B$mean, 0.02), quantile(B$mean, 0.98))
c. After performing the bootstrap, the DJ uses it to compute a 96% confidence interval of (0.21693, 0.42675). What conclusion can be made based on this interval?
Because the null value of _______:
A. is
B. is not
captured by the confidence interval, we should:
A. fail to reject
B. reject
C. accept
D. fail to accept
H0 and conclude that the percentage of songs played by this radio station that are from Canadian artists is:
A. not significantly different
B. significantly different
from what the station states.
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