Final answer:
The data does not suggest that the population mean cholesterol level is 50 mgydL.
Step-by-step explanation:
The question asks if the data suggest that the population mean cholesterol level is 50 mgydL. To determine this, we need to perform a hypothesis test using the sample data provided. We can use a one-sample t-test to compare the sample mean to the hypothesized population mean of 50 mgydL. First, we calculate the sample mean, which is the sum of the data values divided by the number of data points: (58+60+48+55+56+46+54+50+49+51+53+54+53) / 13 = 54.31 mgydL. Next, we calculate the standard deviation of the sample, which measures the spread of the data: √( ( (58-54.31)²+(60-54.31)²+(48-54.31)²+(55-54.31)²+(56-54.31)²+(46-54.31)²+(54-54.31)²+(50-54.31)²+(49-54.31)²+(51-54.31)²+(53-54.31)²+(54-54.31)²+(53-54.31)² ) / (13-1) ) = 3.285 mgydL.
Then, we calculate the t-value using the formula: t = (sample mean - hypothesized population mean) / (sample standard deviation / √sample size) = (54.31 - 50) / (3.285 / √13) = 4.833. We compare this t-value to the critical t-value from the t-distribution table with degrees of freedom equal to the sample size minus 1 (13-1=12) and a significance level (α) of 0.05. If the calculated t-value is greater than the critical t-value, we reject the null hypothesis that the population mean cholesterol level is 50 mgydL.
From the t-distribution table, the critical t-value at α=0.05 with 12 degrees of freedom is 2.179. Since the calculated t-value (4.833) is greater than the critical t-value (2.179), we reject the null hypothesis. Therefore, the data suggests that the population mean cholesterol level is not 50 mgydL.
The correct answer is B) No, the data do not suggest that the population mean cholesterol level is 50 mgydL.