Statistical Practice: One-sample t-test, Two-sample t-test in R

STATISTICAL
PRACTICE

1. One-sample t-test in R
(a) First examine the distribution of the total seconds by doing the following:
i. Produce a histogram of the variable seconds in R and include in your assignment.
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Histogram
Frequency
Bin
Frequency
ii. Describe the distribution of total seconds
Total seconds in the histogram is positively skewed distributed; which indicates more frequency
of less seconds compare to more seconds taken by song to finish.
(b) Perform a one-sample t-test of the null and alternative hypotheses
H0: μ = 240;
Ha: μ 6= 240;
Where μ is the true population mean duration of songs in seconds on
Spotify. To do this, complete the following steps:

i. Perform a one-sample t-test in R and include the output in your assignment
Hypothesized mean
(h):
Sample mean (x):
Sample size:
Sample standard
deviation:
t-statistic: 2.61996
Degrees of freedom: 49
Critical t-value (one-
tailed):
1.67655
1
Critical t-value (two-
tailed): +/- 2.00957524
One-tailed
probability P(h < x):
0.00583
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One-tailed
probability P(h > x):
0.99416
2
Two-tailed
probability P(h = x):
0.01167
5
Two-tailed
probability P(h ≠ x):
0.98832
5
ii. State the value of the test statistic
Value of test statistic = 2.61996
iii. State the P-value
P-value = 0.011675
iv. State the distribution of the test statistic if the null hypothesis is true
The distribution of the test statistic if the null hypothesis is true is 2.61996 at 49 degree of
freedom and 95% significance value.
v. State whether reject or retain the null hypothesis at the 5% significance level?
Justify your decision.
Null hypothesis will be rejected; as p value is lesser than 0.05 (significance level).
3 0 7 . 9 4 7
5 0
3 5 4 . 1 0 0
2 4 0