For this test, the following conditions have been met:
- The sample of 50 posts is a simple random sample. The posts were taken from randomly selected blogs.
- The blogs were searched for the word “anxiety” or any form of it (such as anxious). If no instance of the word was found, a random post from the blog was taken.
- The sample is less than 10% of the population. (There are over 13 billion posts and 35 million blogs on Tumblr).
- The population of blogs on Tumblr has a normal distribution (bell curve).
- After analyzing the 50 blogs, it was found that 60% contain some form of the word “anxiety”.
Key Terms
- Null Hypothesis - The hypothesis that states the observations occur by chance
- Alternative Hypothesis - The hypothesis that states observation are influenced by some non-random cause.
- P-value - The probability of obtaining a sample as extreme as the one that is observed.
- Significance Level - If the p-value is lower than the significance level, the null hypothesis is rejected.
- Standard Deviation - A quantitative value of how each individual observation varies.
- Test Statistic - A numerical summary of the data.
A 1-proportion Z test will be conducted to see if the null hypothesis can be rejected.
Null Hypothesis - 50% of Tumblr users have the word anxiety in their blogs.
Alternative Hypothesis - More than 50% of Tumblr users have the word in their blogs.
The significance level is .10.
To obtain the p-value, the standard deviation must be calculated using the following formula; sqrt(P*(1-p)/n) where P is the hypothesized value of the proportion, which is 50%, and p is the observed value, which is 60%. n represents the sample size which is 50. The standard deviation of this sample is .07.
Next, the test statistic is calculated using the formula (p-P)/standard deviation. It is 1.41. Since the population of posts is normally distributed, the p-value can be obtained by comparing the test statistic to a normal distribution chart.
The p-value is .07, which is less than .10. Therefore, we can reject the null hypothesis, proving that more than 50% of Tumblr users have blogs containing at least one instance of the word anxiety.