Question Details
The following data was collected to determine whether or not Monroe County College students work 18 hours per week:
20,22,25,12,30,49,10,30,17,15,0,24,20,22,23,20,25,24,30,12,15,29,0,25,2,40,30,0,33,0,45,30,38,48,0,40,20,0,0,24.
a) Describe the population
b) Describe the sample
c) State the null hypothesis
d) State the alternative hypothesis
e) Choose the significance level
f) Find the test statistic
g) Find the p-value
h) State your conclusion
i) Explain your findings to a friend who does not understand statistics.
a) The population in this case refers to all Monroe County College students.
b) The sample is the data collected from a subset of Monroe County College students, represented by the list of numbers provided.
c) The null hypothesis states that Monroe County College students work 18 hours per week on average.
d) The alternative hypothesis states that Monroe County College students do not work 18 hours per week on average.
e) The significance level is chosen by the researcher and represents the threshold for determining whether the evidence against the null hypothesis is strong enough to reject it. Common choices for the significance level are 0.05 (5%) or 0.01 (1%).
f) To find the test statistic, we need to determine the appropriate statistical test to use based on the data and the research question. In this case, since we're comparing a sample mean to a known value (18), a one-sample t-test would be appropriate. The test statistic, t, can be calculated using the following formula:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
In this case, we don't have the population standard deviation, so we'll estimate it using the sample standard deviation.
g) To find the p-value, we can refer to a t-distribution table or use statistical software to calculate it. The p-value represents the probability of obtaining a test statistic as extreme as the one calculated (or more extreme) if the null hypothesis is true.
h) Based on the p-value and the chosen significance level, we will either reject or fail to reject the null hypothesis. If the p-value is less than the significance level, we reject the null hypothesis. Otherwise, we fail to reject it.
i) To explain the findings, we can say that the data collected from a sample of Monroe County College students was used to investigate whether they work 18 hours per week on average. By conducting a statistical test, we compared the sample mean to the hypothesized population mean of 18 hours. The test resulted in a test statistic and a p-value. Based on the chosen significance level, we made a decision about the null hypothesis. The conclusion would either be that there is evidence to suggest that Monroe County College students do not work 18 hours per week on average, or that there is not enough evidence to suggest a difference from 18 hours.