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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?
- Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?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? Find the z-table here.
- 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. Based on the 90% confidence interval, (0.02, 0.12), is there convincing evidence that the new formula of laundry detergent is better? A) There is convincing evidence because the interval is entirely above 0. B) There is not convincing evidence because the sample sizes are too small. C) There is convincing evidence because the number of clothing items receiving a…Suppose that X and Y are unknown with E(X) = 20, Var (X) = 4 , E(Y) = 12, and Var (Y) = 16. In addition, suppose that E(XY) = 248. Then what is the correlation of X with Y?An industrial concern has experimented with several different mixtures of the fourcomponents—magnesium, sodium nitrate, strontium nitrate, and a binder—that comprise arocket propellant. The company has found that two mixtures, in particular, give higher flare illumination values than the others. Mixture 1 consists of a blend composed of the proportions.40, .10, .42, and .08, respectively, for the four components of the mixture; mixture 2 consists ofa blend using the proportions .60, .25, .10, and .05. Twenty different blends (10 of each mixture)are prepared and tested to obtain the flare-illumination values. These data appear here (in unitsof 1,000 candles).Mixture 1 185 192 201 215 170 190 175 172 198 202Mixture 2 221 210 215 202 204 196 225 230 214 217a. Plot the sample data. Which test(s) could be used to compare the meanillumination values for the two mixtures?b. Give the level of significance of the test and interpret your findings
- The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.9 8.1 6.9 3.8 2.3 2.7 2.4 0.7 yy 13.9 11.2 9.7 7.2 5.8 6.4 5.9 4.9 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.83x+4.08.y=0.83x+4.08. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 9 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 4 thousand automatic weapons?Answer = Round to 3 decimal places.The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.3 8.6 7.1 3.3 2.4 2.3 2.4 0.7 yy 13.7 11.1 10.4 6.9 6.4 6.2 6.1 4.9 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.83x+4.28.y=0.83x+4.28. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 10.7 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 1.6 thousand automatic weapons?Answer = Round to 3 decimal places.The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.3 8.6 7.1 3.3 2.4 2.3 2.4 0.7 yy 13.7 11.1 10.4 6.9 6.4 6.2 6.1 4.9 xx = thousands of…The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.8 8.6 7.1 3.9 2.5 2.6 2.4 0.4 yy 14.3 11.5 9.8 7.6 6.2 6.5 6.4 4.1 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.86x+4.07.y=0.86x+4.07. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 3 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 4.1 thousand automatic weapons?Answer = Round to 3 decimal places.
