Question

A streaming music site changed its format to focus on previously unreleased music from rising artists. The site manager now wants to determine whether the number of unique listeners per day has changed. Before the change in format, the site averaged 131,520 unique listeners per day. Now, beginning three months after the format change, the site manager takes a random sample of 30 days and finds that the site now has an average of 124,247 unique listeners per day. Using the data provided below, calculate the p-value for the following hypothesis test:
H0:μ=131,520
Ha:μ≠131,520
Listeners after change
125,020
139,250
101,590
94,800
83,700
84,380
139,170
89,380
91,410
139,570
138,980
102,710
124,600
144,770
156,920
131,100
140,020
139,250
118,800
128,380
168,370
133,140
106,930
129,630
120,820
125,250
122,860
122,500
135,230
148,870

Answer 1

Answer:

The p value is: 0.0301

Step-by-step explanation:

Given

$\mu = 131520$

$\bar x = 124247$

$n = 30$

Required

Determine the p value

First, calculate the standard deviation of the given data.

This is calculated as:

$\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}$

So, we have:

$\sigma = \sqrt{\frac{(83700 - 124247)^2 + (84380- 124247)^2 + (89380- 124247)^2 + ..... + (156920- 124247)^2 + (168370- 124247)^2}{30}}$

$\sigma = \sqrt{\frac{13427820070}{30}}$

$\sigma = \sqrt{447594002.333}$

$\sigma = 21156$

The test statistic is then calculated as:

$t = \frac{\bar x - \mu}{\sigma/\sqrt n}$

$t = \frac{124247 - 131520}{21156/\sqrt{30}}$

$t = \frac{-7273}{21156/5.48}$

$t = \frac{-7273}{3860.58}$

$t = -1.88$

The p value is calculated as:

$P(Z > -1.88)$

$P(Z>-1.88) = 0.030054$

$P(Z>-1.88) = 0.0301$ --- approximated.

Hence, the p value is: 0.0301