Determine whether the results below appoar to have statistical significance, and also determine whether the resulls have practical significance , In a study d weight loss program subjects Iost an average 0f 40 Ibs. It is lound thal there About = 21% chance getting Juch resulls with diet that has no eflect. Does the welght loss program have statistical signilicance? No, Ihe program not statistically significant becausa Iho rosulls are unlkely Occi chancu No; the program not statislically signlficant bucause Ine rosulls are Ukely occur by chance; Yes; tho program Slalisticnlly signilicant becauso the rasulls unlikoly OccuI by chnncu Yes, tha pronram statislical signilicant becauso Ihe rosulls Are Ukaly Occur bY chanca Doos tho weight loss program have practical signilicance? Yoa; thu progrom prnctically cionlficant bocauso Iho prount Iat waight Vroo tnouqh coneldored prctcul aan icuali Na, Iho program praclcally elanilchrt bocauso rabu Ukoly Drcmaerhta Ihu wavgnt Ioni prograti Nuu #O onluct No; Ine progrnm practcally wpnlficanl bocouso tho amount wolght Iatt trivml , Yuz, tha prograrn pracically ainificant boc u9t tho rusuli utu t00 unlkoly occuf Dy chance:
Statistical Significance versus Practical Significance The manufacturer of a daily dietary supplement claims that its product will help people lose weight. The company obtains a random sample of 950 adult males aged 20 to 74 who take the supplement and finds their mean weight loss after eight weeks to be 0.9 pounds. Assume the population standard deviation weight loss is $\sigma=7.2$ pounds. (a) State the null and alternative hypotheses. (b) Test the hypothesis at the $\alpha=0.1$ level of significance. Is a mean weight loss of 0.9 pound significant? (c) Do you think that a mean weight loss of 0.9 pounds is worth the expense and commitment of a daily dietary supplement? In other words, does the weight loss have any practical significance? (d) Test the hypothesis at the $\alpha=0.1$ level of significance with $n=40$ subjects. Assume that the sample mean weight loss is still 0.9 pounds. Is a sample mean weight loss of 0.9 pounds significantly more than 0 pounds? Conclude that large sample sizes cause $P$ values to shrink substantially, all other things being the same.
So four people lost 45 lb And there is a probability of 30% of that happening with no diet at all. Um so this this is pretty high for it to happen randomly by chance. So it's not gonna be It's not statistically significant because of that 30%. However, it could be have some practical application practical significance just because £45 is a lot so some practical but no statistical significance. Yeah.
It's a kind of an interesting question if we we would be assuming that the anxiety level if we are going from easy to difficult is equal to the anxiety level. If the questions were difficult to easy and alternately, we just want to know if there's a difference and easy to difficult and not equal to difficult to easy. And so we're going to assume that that difference is actually zero so that the, I'll just write E G minus D. E. That that difference is zero. And when I put this into my calculator, um we have the lists have different sample sizes. We have that first group of the E. T. D. I have, there are 25 numbers versus the D two E. There are 16 numbers and we could use the degrees of freedom of 15, but I'm going to use the degrees of freedom from the formula. And that degrees of freedom ends up being uh 30 almost 39. So 38 point well, I'm just going to call it 39 it's approximately 39 degrees of freedom. And that test statistic that we're going to get, we need to take the mean, which was 27.1152 minus the mean of the other group, which was 31.7 to 8125 And then divided by the square root of. And the first standard deviation all around that a bit is 6.857 one square, divided by the sample size, which was 25. And then the second standard deviation was 4.26 square divided by the sample size of 16. And when I got that test statistic, the test statistic came out to be, I'll just read it up here negative 2.6 566 And so it came out down here. And since we're doing a two tailed test, we also use this one. And so what's the likelihood of getting a test statistic in this distribution that is less than or equal to that negative 2.6566 That gives us this tale and then we want the other tales to double it. And that p value comes out to be a 0.114 So at a 5% significant level, this is smaller than 5%. So we would have sufficient evidence to reject now. Yeah. And say that the mean anxieties are different so that they're different. The means are different. However, at a 1% significance level we would fail to reject the novel. Mhm. And we'd have to say here that they're actually not. They appeared to be the same. So it does depend on our significance level. How did pick you want to be. But it is an interesting idea in all my years of teaching, I never thought about the arrangement of having them all go easy, too difficult or difficult to easy. So what interesting concept.
In this question, we want to check whether the results appear to have statistical as well as practical significance. It is given that in a study off the Kingman diet and exercise program, 40 subjects lost and average off £22 and it is given that there is only 1% chance off getting such results with the program that has no effect in the future, you all will learn about the values and Alfa level. In this case, the Alfa level is zero point. Sorry. In this case, the P value is 0.1 which means that if this program were not to be effective or if this program is really not effective, there is only 1% chance that this kind of result can be seen. So let's see if our AL 50.5 if our AL 50.5 this p values 0.1 which means that it is less an Alfa and hence we can say that we have statistically significant are statistically significant evidence to say that we can reserve the null hypothesis. What is the hypothesis? The hypothesis in this case would be the null hypothesis would be that there is no effect, that there is no effect. And the alternative would be the opposite of this alternative would be that this is effective, that this is an effective program. So, yes, Statistically, this does seem to have an effect. Or we can say that statistically, this does seem to be a significant what we can say. Significant result. And what about practical significance? 40 subjects lost. Lost 10 every day for what? £22. It is quite possible. So, yes, This also appears to be practically significant because, yes, if there is a very good program, if they have a good diet, if they have a good exercise regime, it is quite possible that they lose £22. So, yes, this is practically as well a statistically significant, and these are our chances.
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