A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Assuming the conditions for inference are met, what is the 90% confidence interval for the difference in proportions of clothes that receive a rating of 7 or higher for the two detergents?

A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Assuming the conditions for inference are met, what is the 90% confidence interval for the difference in proportions of clothes that receive a rating of 7 or higher for the two detergents?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 18E

See similar textbooks

Similar questions

The population Pinmillions of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?
The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?
2. Find the linearization of √x at a = 49. Then use your linearization to approximate √56.
Find the moment generating function for Y. c=4
A cup of water at an initial temperature of 81°C is placed in a room at a constant temperature of 24°C. The temperature of the water is measured every 5 minutes during a half-hour period. The results are recorded as ordered pairs of the form (t, T), where t is the time (in minutes) and T is the temperature (in degrees Celsius). (0, 81.0°), (5, 69.0°), (10, 60.5°), (15, 54.2°), (20, 49.3°), (25, 45.4°), (30, 42.6°) (a) Subtract the room temperature from each of the temperatures in the ordered pairs. Use a graphing utility to plot the data points (t, T) and (t, T − 24). (b) An exponential model for the data (t, T − 24) is T − 24 = 54.4(0.964)t. Solve for T and graph the model. Compare the result with the plot of the original data. (c) Use a graphing utility to plot the points (t, ln(T − 24)) and observe that the points appear to be linear. Use the regression feature of the graphing utility to fit a line to these data. This resulting line has the form ln(T − 24) = at + b, which is…
An excerpt of the t table with 57 degrees of freedom is given below. Degreesof Freedom Area in Upper Tail 0.20 0.10 0.05 0.025 0.01 0.005 57 0.848 1.297 1.672 2.002 2.394 2.665 The t table gives the area in the upper tail of the curve, so only positive values of t are given. However, this curve is symmetric about 0 so the area in the upper tail is the same as the area in the lower tail for a given number of degrees of freedom. That is, for 57 degrees of freedom, the area in the lower tail, left of t = −1.190, will be the same as the area in the upper tail, right of t = 1.190. We will first determine a range of the p-value corresponding to the upper tail. The columns represent the area in the upper tail of the curve and the rows represent the degrees of freedom. The values within the table are values of t. Moving along the row for 57 degrees of freedom, note that the exact value of the test statistic, t = 1.190, is not in this row. However, it is directly between the values of…
Find the DE like in the example
b. At α = 0.05, test your hypothesis. Show all your calculations to receive full credit.
Find the Fourier series representation of the periodic function f(x) = cx2 + d if -π < x < π if c = 1.16 and d = 9.8. Then, find the value of a0.
Identify the direction of increase in z in each of the following case cases:
4a. Determine the laplace transform
3. Integrate the following by hand