Hypothesis test for one population proportion Archives

Hypothesis test for one population proportion

Consider the following hypothesis test:

$H ₀ : π \leq 0.75$ $H ₁ : π > 0.75$ In a sample of 100, the sample proportion is 0.83. Calculate the p-value for the test and choose the correct answer from the list of options below: a) 0.1251b) 0.0322c) 0.0516d) 0.0045e) 0.0433…

Hypothesis test for one population proportion

A manufacturer of candy would like to know whether its bag filling machine works correctly at the 300 gram setting. It is believed that the machine is overfilling the bags. A 13 bag sample had a mean of 308 grams with a variance of 81. 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 $(μ) = 300$ The Sample Mean $(\bar{x}) = 308$ The Sample Variance $(s^{2}) = 81$ The Sample Size $(n) = 13$ $∴$ The Sample Standard Deviation $ (s) = \sqrt{81} = 9…

Hypothesis test for one population proportion

Microwave Cooking A survey of 100 households found that 70% use the microwave to prepare their meals. Find the 95% confidence interval for the proportion. Use Excel and round the answers to three decimal places.

Answer:Given:The sample proportion $(\hat{p}) = 0.70$ The sample size $(n) = 100$ The confidence interval level $= 95 %$ Solution:The significance level $(α) :$ $α = 1 - 0.95$ $= 0.05$ The…

Hypothesis test for one population proportion

Microwave Cooking A survey of 90 households found that 65% use the microwave to prepare their meals. Find the 95% confidence interval for the proportion. Use Excel and round the answers to three decimal places.

Answer:Given:The sample proportion $(\hat{p}) = 0.65$ The sample size $(n) = 90$ The confidence interval level $= 95 %$ Solution:The significance level $(α) :$ $α = 1 - 0.95$ $= 0.05$ The…

Hypothesis test for one population proportion

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 $(α) = 0.05$ Solution:The null and alternative hypothesis: $ H_0:…

Hypothesis test for one population proportion

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 $(α) = 0.05$ Solution:The null and alternative hypothesis: $ H_0:…

Hypothesis test for one population proportion

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 $(α) = 0.05$ Solution:The null and alternative hypothesis: $ H_0:…

Hypothesis test for one population proportion

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 $(α) = 0.05$ Solution:The null and alternative hypothesis: $ H_0:…

Hypothesis test for one population proportion

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 $(α) = 0.05$ Solution:The null and alternative hypothesis: $ H_0:…

Hypothesis test for one population proportion

A publisher reports that 45% 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 48% 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 $(p) = 0.45$ The Sample Proportion $(\hat{p}) = 0.48$ The Sample Size $(n) = 410$ The Level of significance $(α) = 0.05$ Solution:The null and alternative hypothesis: $ H_0:…