Question

question 1
according to facebooks self - reported statistics, the average facebook user is connected to 80
community pages, groups, and events. for a statistics project, a student at contra costa college
tests the hypothesis that ccc students will average less than 80 such connections.
she posts a survey on her facebook page. her sample contains 45 responses.
she chooses a 5% level of significance. from her data she calculates a t - test statistic of approximately - 1.74 with a p - value of about 0.04.
what can she conclude?
a. nothing. the conditions for use of a t - test are not met. she cannot trust that the p - value is accurate for
this reason.
b. the data is statistically significant. in other words, the data do provide enough evidence to conclude that
the mean number of facebook connections to community pages, groups and events of all all ccc college
students is less the 80.
c. the data is not statistically significant. in other words, the data do not provide enough evidence to
conclude that the mean number of facebook connections to community pages, groups and events of all ccc
college students is less the 80.

Explanation:

To determine the conclusion, we compare the P - value with the significance level. The significance level ($\alpha$) is 0.05. The P - value is 0.04. Since \(P - value=0.04<\alpha = 0.05\), we reject the null hypothesis. When we reject the null hypothesis, the data is statistically significant. This means the data provides enough evidence to support the alternative hypothesis (in this case, that the mean number of connections is less than 80).
Also, for a t - test, one of the main conditions (when the population standard deviation is unknown) is that the sample is a simple random sample. Here, the sample is from a Facebook page survey (not a simple random sample of all CCC students). But if we assume that despite the sampling method flaw, we are just going by the P - value vs significance level rule (as per the options given which include a statistical significance option), we note the P - value and significance level comparison.

Answer:

B. The data is statistically significant. In other words, the data do provide enough evidence to conclude that the mean number of Facebook connections to community pages, groups and events of all all CCC college students is less the 80.