Question

a statistics student wanted to test the claim that students have a mean higher than 130 facebook friends. from her randomly collected survey data, the statistics student calculates that the mean number of facebook friends for her sample is 138.7. she analyzed her data using a z - test and obtained a p - value of 0.23. what conclusion can she draw from her data?
○ nothing. the conditions for use of a z - test were not met. she cannot trust that the p - value is accurate for this reason.
○ even though 138.7 is larger than 130, it is not significantly larger than 130. in other words, the data do not provide enough evidence to conclude that the mean number of facebook friends of all ccc college students is higher than 130.
○ 138.7 is significantly larger than 130. in other words the data provide enough evidence to conclude that the mean number of facebook friends of all ccc college students is higher than 130.

Explanation:

To determine the conclusion, we analyze the p - value (0.23) and the conditions for a z - test. A p - value of 0.23 is relatively large (typically, we use a significance level like α = 0.05). A large p - value means we fail to reject the null hypothesis (that the mean is 130 or less). Also, we need to check if the conditions for a z - test are met. If the conditions (like knowing the population standard deviation, having a large enough sample size for the Central Limit Theorem to apply, etc.) are not met, the p - value from the z - test is not accurate. But in the context of the options, the key is about the significance of the result. Since the p - value (0.23) is greater than common significance levels (e.g., 0.05), the sample mean of 138.7, although larger than 130, is not significantly larger. So the data does not provide enough evidence to conclude that the mean number of Facebook friends of all CCC college students is higher than 130.

Answer:

Even though 138.7 is larger than 130, it is not significantly larger than 130. In other words, the data do not provide enough evidence to conclude that the mean number of Facebook friends of all CCC college students is higher than 130.