A manufacturer of popcorn would like to know whether its bag filling machine works correctly at the 350 gram setting. It is believed that the machine is overfilling the bags. A 15 bag sample had a mean of 360 grams with a variance of 121. Assume the population is normally distributed. Is there sufficient evidence at the 0.01 level that the bags are overfilled?

Answer:Given:The Hypothesized Mean $ (\mu) = 350 $The Sample Mean $ (\bar{x}) = 360 $The Sample Variance $ (s^2) = 121 $The Sample Size $ (n) = 15 $ $\therefore$ The Sample Standard Deviation $ (s) = \sqrt{121} = 11…

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 500 gram setting. It is believed that the machine is overfilling the bags. A 12 bag sample had a mean of 510 grams with a variance of 144. Assume the population is normally distributed. Is there sufficient evidence at the 0.05 level that the bags are overfilled?

Answer:Given:The Hypothesized Mean $ (\mu) = 500 $The Sample Mean $ (\bar{x}) = 510 $The Sample Variance $ (s^2) = 144 $ $\therefore$ The Sample Standard Deviation $ (s) = \sqrt{144} = 12 $The Significance Level $ (\alpha) = 0.05…

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 411 gram setting. It is believed that the machine is overfilling the bags. A 10 bag sample had a mean of 417 grams with a variance of 169. Assume the population is normally distributed. Is there sufficient evidence at the 0.02 level that the bags are overfilled?

Answer:Given:The Hypothesized Mean $ (\mu) = 411 $The Sample Mean $ (x\bar) = 417 $The Sample Variance $ (s^2) = 169 $ $\therefore $ The sample Standard deviation $(s) = \sqrt(169) = 13 $The Significance Level $ (\alpha) = 0.02…

A publisher reports that 53% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually over the reported percentage. A random sample of 420 found that 56% of the readers owned a personal computer. Is there sufficient evidence at the 0.05 level to support the executive’s claim?

Answer: Given Data:Hypothesized Population Proportion $ (p) = 0.53 $The Sample Proportion $ (\hat{p}) = 0.56 $The Sample Size $ (n) = 420 $ The Level of significance $ (\alpha) = 0.05 $ Solution:The null and alternative hypothesis: $ H_0:…

A publisher reports that 51% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually over the reported percentage. A random sample of 410 found that 54% of the readers owned a personal computer. Is there sufficient evidence at the 0.05 level to support the executive’s claim?

Answer: Given Data:Hypothesized Population Proportion $ (p) = 0.51 $The Sample Proportion $ (\hat{p}) = 0.54 $The Sample Size $ (n) = 410 $ The Level of significance $ (\alpha) = 0.05 $ Solution:The null and alternative hypothesis: $ H_0:…

A publisher reports that 47% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually over the reported percentage. A random sample of 430 found that 50% of the readers owned a personal computer. Is there sufficient evidence at the 0.05 level to support the executive’s claim?

Answer: Given Data:Hypothesized Population Proportion $ (p) = 0.47 $The Sample Proportion $ (\hat{p}) = 0.50 $The Sample Size $ (n) = 430 $ The Level of significance $ (\alpha) = 0.05 $ Solution:The null and alternative hypothesis: $ H_0:…

A publisher reports that 44% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually over the reported percentage. A random sample of 370 found that 47% of the readers owned a personal computer. Is there sufficient evidence at the 0.05 level to support the executive’s claim?

Answer: Given Data:Hypothesized Population Proportion $ (p) = 0.44 $The Sample Proportion $ (\hat{p}) = 0.47 $The Sample Size $ (n) = 370 $ The Level of significance $ (\alpha) = 0.05 $ Solution:The null and alternative hypothesis: $ H_0:…

A publisher reports that 55% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually over the reported percentage. A random sample of 400 found that 58% of the readers owned a personal computer. Is there sufficient evidence at the 0.05 level to support the executive’s claim?

Answer: Given Data:Hypothesized Population Proportion $ (p) = 0.55 $The Sample Proportion $ (\hat{p}) = 0.58 $The Sample Size $ (n) = 400 $ The Level of significance $ (\alpha) = 0.05 $ Solution:The null and alternative hypothesis: $ H_0:…