Before bringing a new product to market, firms carry out...

Before bringing a new product to market, firms carry out extensive studies to learn how consumers react to the product and how best to advertise its advantages. Here are data from a study of a new laundry detergent.29 The participants are a random sample of people who don’t currently use the established brand that the new product will compete with. Give subjects free samples of both detergents. After they have tried both for a while, ask which they prefer. The answers may depend on other facts about how people do laundry. (a) How are laundry practices (water hardness and wash temperature) related to the choice of detergent? Make an appropriate graph to display this relationship. Describe what you see. (b) Determine whether or not the sample provides convincing evidence that laundry practices and product preference are independent in the population of interest.

Before bringing a new product to market, firms carry out extensive studies to learn how consumers react to the product and how best to advertise its advantages. Here are data from a study of a new laundry detergent.29 The participants are a random sample of people who don’t currently use the established brand that the new product will compete with. Give subjects free samples of both detergents. After they have tried both for a while, ask which they prefer. The answers may depend on other facts about how people do laundry.
(a) How are laundry practices (water hardness and wash temperature) related to the choice of detergent? Make an appropriate graph to display this relationship. Describe what you see.
(b) Determine whether or not the sample provides convincing evidence that laundry practices and product preference are independent in the population of interest.

Key Concepts

Contingency Tables

Contingency tables are used to organize and analyze data from two or more categorical variables by displaying the frequency counts at each combination of category outcomes. In studies like this, they help summarize how different groups (such as those distinguished by laundry practices) prefer one product over another, providing a structured way to examine potential associations between the variables.

Graphical Representation of Categorical Data

Graphical methods, such as bar charts, mosaic plots, or segmented bar graphs, provide visual summaries of the relationship between categorical variables. These visualizations help detect patterns, trends, or differences among groups (for instance, different laundry practices) in product preference, making it easier to interpret the data and communicate findings to stakeholders.

Chi-Square Test of Independence

The chi-square test of independence is a statistical test used to determine whether there is a significant association between two categorical variables. By comparing the observed frequencies in the contingency table with the expected frequencies under the assumption of independence, researchers can assess if factors like laundry practices are related to product preference in a statistically meaningful way.

Hypothesis Testing

Hypothesis testing is a systematic method used to decide whether there is enough evidence in a sample of data to infer that a certain condition holds for the entire population. In this context, the null hypothesis might state that laundry practices and product preference are independent, and through the test, conclusions can be drawn regarding the validity of this assumption based on sample data.

Transcript

00:03 All right, so this problem, we have, we're giving a set of data concerning people's water choice or water method of washing their laundry, given whether they use the standard or new detergent.

00:20 It's this table up top.

00:22 I went ahead and already turned that into a table of percentages with respect to their rows, just because we're going to need to do that anyway, and it's just a bunch of calculator work.

00:32 Okay, so we did that.

00:33 And now we need to graph and summarize these percentages.

00:36 So these are percentages you should have here versus percent.

00:41 So let's grab this.

00:56 Percents.

01:05 All righty.

01:13 Percents.

01:18 All right.

01:18 And then we need, what's our highest percent? our highest percent is in the 30s, so i don't need to bother making this higher than five.

01:27 So 10, 20, 30, 40, 40.

01:32 40, 50, and there's a percentage and then we need to know if they did.

01:45 Okay, so we'll have standard and new will be, so we'll have detergent type and then we will have, i said water, but i guess technically it's your wash type, even though it's the type of water using that defines the wash type.

02:06 So i guess you could do whatever you want.

02:10 All right.

02:10 So standard new 35 and 31.

02:18 35.

02:25 31.

02:31 All right.

02:31 And then we have all right.

02:35 If i say the type.

02:36 That was soft water.

02:41 Oh, i forget what i labeled them.

02:46 Crap soft water warm wash that's what the w was soft water warm wash i forgot what my w stood for all right and then we're gonna have standard new soft water hot wash 18 and 14 standard new hot water warm wash 28 and 34 and the last one hot water hot wash 0 .2 and point 2 .1.

04:24 All right.

04:25 And that's standard and that is new.

04:28 So there is our graph.

04:33 Sorry if my writing's a little sloppy.

04:34 It looks like i had more room than i thought i would.

04:36 I was prepared for this to be really cramped, but it's actually not too bad.

04:39 Anyway, we're supposed to now summarize our results.

04:42 So let's look at this graph.

04:43 If we look at this graph, it looks like well there's a couple things it looks like people were most likely to use the standard people were most likely to use standard detergent if they they also used soft water hot wash.

05:38 Oh wait, i did the wrong one, didn't i? that's not true.

05:41 If they used hot water warm wash, this one.

05:49 I might keep messing it up.

05:50 My bad.

05:51 I keep writing down the initials, but looking at the wrong picture when i do.

05:55 They're most likely to use the standard detergent if they used this one, which is soft water, warm wash.

06:01 There we go my bad i keep mixing myself up okay and they were they were most likely to use new detergent if they also used all right new detergent it looks like that one.

06:42 That's what i give is because being mixed up.

06:43 Nuturgent, that's gonna be this guy.

06:45 That is gonna be the hot water warm wash.

06:48 Hot water warm wash.

06:51 Okay, there's our highs and lows.

06:53 So we did that.

06:54 Just to make sure that i did that correct, this point three, four should be the highest new, and that's definitely true, and this should be the highest standard, and that's definitely true.

07:03 So i did that correctly.

07:05 All right, now let's see is buying preference independent of wash choice? so for part b, we needed do we want to do a kai square test but we need to do some things first so our null hypothesis is that on detergent preference is independent of um washed preference when i say wash preference we're talking about the type of water wash they're using and then the alternate hypothesis would just be that that the detergent preference is not independent of wash preference.

08:05 So we just copy and paste into that sentence.

08:14 Okay.

08:20 Now we need to, we did pictures.

08:26 So we did that.

08:28 Okay, yeah, i mean, now we need to do the kai squared.

08:31 Conditions, kai squared conditions.

08:42 Okay, so the kye squared conditions are random.

08:54 Well, the data came from a random sample.

09:12 To tell us that in the setup of the problem, that it was a randomized experiment...