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Numerade Educator



Problem 71 Easy Difficulty

Use a computer to compare a random sample to the population from which the sample was drawn. Consider the normal population with mean 100 and standard deviation 16.
a. List values of $x$ from $\mu-4 \sigma$ to $\mu+4 \sigma$ in increments of half standard deviations and store them in a column.
b. Find the ordinate $(y$ value) corresponding to each abscissa $(x$ value) for the normal distribution curve for $N(100,16)$ and store them in a column.
c. Graph the normal probability distribution curve for $N(100,16).$
d. Generate 100 random data values from the $N(100,16)$ distribution and store them in a column.
e. Graph the histogram of the 100 data obtained in part d using the numbers listed in part a as class boundaries.
f. Calculate other helpful descriptive statistics of the 100 data values and compare the data to the expected distribution. Comment on the similarities and the differences you see.



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Video Transcript

{'transcript': "All right, That's the question. 1 83 So in this question, our simple size and IHS 50 are a We moved to the question part So part A what is a no hypothesis? So here the now hypothesis iss the population mean the population mean is 100. And if we use me to represent the population means so our no hypothesis is going to be your equivalent to say, um us Equal Teoh 100. All right, Part B, what is the alternative hypothesis? So here we can say the population means is not 100 or we just say mu does not equal to 100 note. Here it is a not be close eye. So when we considering the peat p value winning to consider two tails together, just keep in mind. All right, heart, see what's value for Alfa here in the question it is stating that using a airplane there a one level of significance. So that means our Alfa is going to be there a point there or what? All right, um, de what is a hypothesized, uh, value from you? So has wasted in the part a, um in the no hypothesis, our hypothesized highly valuable for me was going to be 100. Okay, part A what? Ihsaa value for ex parte um, export. Here it ISS represents the Sam Pony, and it is given in a question. On the better is 96. All right, heart f What is a standard deviation? They're here. Siegel eyes representing the standard deviation TV's. Okay. And, uh, and as equal to 12 partying siga off export. Here it is representing the standard arrow center era off. I mean and by the formula Friends, it is equal to speak on Monday, but Abay Square showed up in, so it's going to be 12 over square. Oh, no. 50. It is equal to 1.7 Terrible. All right. And we moved to h. We're interested in the testes. Statistic is that star. So we need to do some calculation here. According to the former learns that that start is equal to x bar minus the hypothesized value over mu over Segolela divided by square enough. And so we just plug in numbers. We have 96 minus 100 divided by 12 over Square Rudo 50 and it is equal. Teoh Negative 2.36 All right, what is the What is a P value here? The P value is going to be the probability off a random bearable that which absolute value is greater than or equal to the absolute value of ours that start Or, in another words, it issue. Go to the probability off a stunner. Normal, um, random bearable. That which ISS smaller than or equal to negative 2.36 So this is our of value for its that star. Plus the probability off is that greater than our equal? Teoh? Positive 2.36 All right, if we draw occur, representing the center normal distribution in here and it is going to be negative. Teoh calling 36 and symmetrical way Here it is. Positive 2.36 So our Peabody, who is going to be the summation off the area for this Tau and the sheriff of this tale as well? The ended up and equal Teoh the P value. So this, um, south is equal. Teoh Narrow point narrow 18 All right, Pant heart J wants a physician. So we were going to compare p value with our level of significance with the Alfa I recall Alfa is U Boat Teoh. There a point there. What? And hear? The P value is equal to their opined there. 018 And obviously our people I always greater than Alfa So here we are fell Teoh reject the null hypothesis."}