Analysis of Lead Content in Lip Products: Lipstick vs Lip Gloss

For this question, return to the data set on lead content in lip products, in the Excel spreadsheet Lead Data.xlsx on Courselink1 . A reminder that the columns in the data set are: Column 1 : Sample Code. A unique identifying code for each lip product in the sample Column 2 : Country of Purchase. Where the lip product was purchased Column 3 : Production Country. Where the lip product was produced. Column 4 : Average Lead Content (Pb) in units of mg/kg. The average amount of lead measured in 6 replicates of each lip product in the sample Column 5 : Standard Deviation of Lead Content (Pb) in units of mg/kg. The standard deviation in the amount of lead measured in 6 replicates of each lip product in the sample Column 6 : Shade. The shade of the lip product Column 7 : Lip Product Type. LP = lipstick, LG = lip gloss Column 8 : Price Category. 1 =“low”, 2 = “medium”, 3 = “high” For the purposes of this analysis, we will assume that each row of the data set represents a randomly selected lip product. We are interested in the lead content (Column 4) and Lip Product type (Column 7). Previously, we had looked at lip products in general. This time, we will consider lipstick and lip gloss as separate groups of lip products. Our interest is in determining if the mean amount of lead is the same in these two types of lip products, or if there is evidence of a difference in the mean amount of lead content between the two types of products at the 5% level of significance. For clarity, we will consider lipstick to be Group #1 and lip gloss to be Group #2. Create a histogram and a side-by-side boxplot of lead content for each type of lip product, and include all three plots in your report. Include with your plots a commentary on the shape of the distribution in both groups, if there are outliers in the sample, and any other relevant observations. Using the side-by-side boxplot, comment on whether or not there appears to be a difference in the mean amount of lead in lipstick versus lip gloss products. If so, which product to you suspect has the higher amount of lead? Explain how you reached your conclusion. State the null and alternate hypotheses that would be appropriate for the research question of interest. Using the appropriate function in the Data Analysis Toolpak, conduct a hypothesis test using the Welch Approximate t Procedure. Include, in your report, the output you get from this procedure. Using the output from Excel, clearly state the value of the test statistic and p-value in your report. Use the p-value to decide regarding your null hypothesis (i.e. is it rejected or not rejected?) at the 5% level of significance. Include this decision, as well as a final conclusion about your hypothesis test, in your report. Now, create a 95% confidence interval for the difference in mean lead content between lipstick and lip gloss products. You can use the summary statistics (i.e. X¯ 1, X¯ 2, s1, and s2) obtained from the Excel output, as well as the rounded degrees of freedom that are provided, to create your confidence interval. You do not need to show every step of your calculation in your report, however you must clearly state the summary statistics and confidence coefficients