To compare freshmen's knowledge of history, samplesof 50 freshmen from each of twouniversities were given a special test. Those from the firstuniversity have a...

At Western University the historical mean of scholarship examination scores for freshman applications is $900 .$ A historical population standard deviation $\sigma=180$ is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.
a. State the hypotheses.
b. What is the 95$\%$ confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean of $\overline{x}=935 ?$
c. Use the confidence interval to conduct a hypothesis test. Using $\alpha=.05,$ what is your conclusion?
d. What is the $p$ -value?

This is the section for men with news has the amendment. Neo test is a non parametric alternative to the T test for the difference between two independent means. This test is often used in situations in which the two symbols are thrown from the same population off subject but different treatments. Treatments are used on each sense. For I'm about 27 are quite to find the critical values for there's giving hypotheses. For number eight, we a Cuban and a is it crawled through 18 and be It's called to game, and our alpha is a quote to 0.5 So to find the critical value you critical we use table that didn't be Andi using to didn't be we find you critical is less than and close to 88. So this is 18 from a B. We have been one Equality 78 and to cultures 45 and our FA is a quote soon 0.0, right, Since our since we have been one and two greater than 20 mhm, you can find the critical value from so you didn't be. We use these that value right to find the critical video which is pure feeling. So we used Alfa as the accumulative probability. So we need to find that off Alfa and which is equal to that 0.0 fight and using table three we consider it that's are far is negative one point six five and we need to find the people PV king off. Is it less than or equal to negative? 1.65 is a culture zero point 04 95 is a critical V.

20 every day. The non hypothesis is that new one in smaller than or equal to Muto and the alternative high Busses that me one is bigger than mute. So the critical values are the values in Table four, corresponding to mobility on 1.9. So that is even toe 1.3. So the rejection reasons contain all very is larger than 1.28 So this tested statistics X one bar 162 minus mu one minus muto over squared off symbol on the square over anyone plus Sigma squared over and to which approximately equal to four point always so if the value of testing is within the rejection rating than not, have also rejected. So as UH, two point or seven is bigger than 1.28 So you reject the not hypothesis, so there is sufficient evidence to support that.

In this problem, we want to determine the critical value for a two tailed tests. That is a hypothesis test regarding population means you where the standard deviation of the population sigma is known as alpha equals 20.5 significance of confidence. This question is shown your understanding of hypothesis tests for population mean with single known particularly is testing our knowledge of how to identify the critical value for use of a classical approach to testing. So we're looking for the critical value for a two tailed tests that separates the area and the two tails for 20.0 to 5 where xenon and negatives and not have the same absolute value. So to find the critical value that leaves area in each tail 50.25 we need to use a table to find Z. Such that the probably easy greater than 0.25 So from such as the table, we find that probably easy less than negative zero equals 0.25 Which is the equivalent to the probability gives critical Z score plus or minus 1.96 That is, our zenon is 1.96 or negative. Xenon is negative 1.96

This'll question says, Find the Cisco's that correspond to each value and determine whether any of these valleys unusual. Okay, The sad is an exam used by colleges and universities to evaluate undergraduate students. The tests are normally distributed Discourse on normal distributed in a recently of the meter score Waas 1498 new is equal to 1498 Okay, standard deviation is 316 316 Makes sense. The Tesco's off four students selected random are 1920 2040 19 2012 40 not 2040 12 14 2200 and 13 90 2200 and 13 90. Okay, these are the four scores that we have now. We want to find the Zed School in order to find the set score. The formula is expire minus mu upon sigma. What is expert? It is the mean off 1920 12 40 2200 and 13 90 divided by food. So just a moment. So I have to find the mean off this food that is 1920 plus 12 40 plus 2200 plus 13 19 And this is divided by four. So this is +1687 So this is +1687 minus what was the mean one? +4981498 upon 316 upon 316 So this is going to be 1687 minus 1498 divided by 316 This is turning out to be zero point 59 This is turning out to be zero point 598 Or I can write this a 0.6 approximately equal to 0.6 and we will find that this is not unusual, right? The P value for this will be very high. If I calculate this, we will look for zero point by 98 approximately comes out to be 0.274 So this is my normal distribution. This is 0.60 point six. This area is 60.274 So the zero point 274 So this is not unusual. This is my Z statistic. And if I want to find the area, this is my area approximately