Questions: The following data represent the pulse rates (beats per minute) of nine students enrolled in a statistics course. Treat the nine students as a population. Complete parts (a) to (c) Student Pulse ------ Perpectual Bempah 90 Megan Brooks 87 Jelt Honeycutt 86 Clarice Jelforson 88 Crystal Kurtentach 63 Janette Lantha 62 Kevin McCarthy 73 Tamny Ohm 75 Katty Woldya 89 (a) Determine the population mean pulse. The population mean pulse is approximately 79.2 beats per minute. (Type an integer or decimal rounded to the nearest tenth as needed.) (b) Determine the sample mean pulse of the following two simple random samples of size 3. Sample 1: Janette, Clarice, Perpectual Sample 2: Kevin, Megan, Clarice The mean pulse of sample 1 is approximately 80 beats per minute. (Round to the nearest tenth as needed) The mean pulse of sample 2, is approximately 82.7 beats per minute. (Round to the nearest tenth as needed) (c) Determine if the means of samples 1 and 2 overestimate, underestimate, or are equal to the population mean

The following data represent the pulse rates (beats per minute) of nine students enrolled in a statistics course. Treat the nine students as a population. Complete parts (a) to (c) Student Pulse ------ Perpectual Bempah 90 Megan Brooks 87 Jelt Honeycutt 86 Clarice Jelforson 88 Crystal Kurtentach 63 Janette Lantha 62 Kevin McCarthy 73 Tamny Ohm 75 Katty Woldya 89 (a) Determine the population mean pulse. The population mean pulse is approximately 79.2 beats per minute. (Type an integer or decimal rounded to the nearest tenth as needed.) (b) Determine the sample mean pulse of the following two simple random samples of size 3. Sample 1: Janette, Clarice, Perpectual Sample 2: Kevin, Megan, Clarice The mean pulse of sample 1 is approximately 80 beats per minute. (Round to the nearest tenth as needed) The mean pulse of sample 2, is approximately 82.7 beats per minute. (Round to the nearest tenth as needed) (c) Determine if the means of samples 1 and 2 overestimate, underestimate, or are equal to the population mean
Transcript text: The following data represent the pulse rates (beats per minute) of nine students enrolled in a statistics course. Treat the nine students as a population. Complete parts (a) to (c) \begin{tabular}{l|c} \hline Student & Pulse \\ \hline Perpectual Bempah & 90 \\ Megan Brooks & 87 \\ Jelt Honeycutt & 86 \\ Clarice Jelforson & 88 \\ Crystal Kurtentach & 63 \\ Janette Lantha & 62 \\ Kevin McCarthy & 73 \\ Tamny Ohm & 75 \\ Katty Woldya & 89 \end{tabular} (a) Determine the population mean pulse. The population mean pulse is approximately 79.2 beats per minute. (Type an integer or decimal rounded to the nearest tenth as needed.) (b) Determine the sample mean pulse of the following two simple random samples of size 3. Sample 1: {Janette, Clarice, Perpectual} Sample 2: {Kevin, Megan, Clarice} The mean pulse of sample 1 is approximately 80 beats per minute. (Round to the nearest tenth as needed) The mean pulse of sample 2, is approximately 82.7 beats per minute. (Round to the nearest tenth as needed) (c) Determine if the means of samples 1 and 2 overestimate, underestimate, or are equal to the population mean
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Solution

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Solution Steps

Step 1: Calculate the population mean pulse.

The population mean is the sum of all the pulse rates divided by the number of students: (90 + 87 + 86 + 88 + 63 + 62 + 73 + 75 + 89) / 9 = 713 / 9 ≈ 79.2

Step 2: Calculate the sample mean pulse for Sample 1.

Sample 1 consists of Janette (62), Clarice (88), and Perpectual (90). The sample mean is (62 + 88 + 90) / 3 = 240 / 3 = 80.

Step 3: Calculate the sample mean pulse for Sample 2.

Sample 2 consists of Kevin (73), Megan (87), and Clarice (88). The sample mean is (73 + 87 + 88) / 3 = 248 / 3 ≈ 82.7

Step 4: Compare sample means to the population mean.

The population mean is approximately 79.2. Sample 1's mean is 80, which is slightly higher than the population mean. Sample 2's mean is 82.7 which is higher than the population mean.

Final Answer

(a) Population mean pulse: 79.2 bpm (b) Sample 1 mean pulse: 80 bpm; Sample 2 mean pulse: 82.7 bpm (c) Sample 1 mean _overestimates_ the population mean. Sample 2 mean _overestimates_ the population mean.

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