hypothesis testing problems and their solution
Answers
Step-by-step explanation:
1)It is believed that the average level of prothrombin in a normal population is 20 mg/100 ml of blood plasma with a standard deviation of 4 miligramos/100 ml. To verify this, a sample is taken from 40 individuals in whom the average is 18.5 mg/100 ml. Can the hypothesis be accepted with a significance level of 5%?
solution:
It is believed that the average level of prothrombin in a normal population is 20 mg/100 ml of blood plasma with a standard deviation of 4 miligramos/100 ml. To verify this, a sample is taken from 40 individuals in whom the average is 18.5 mg/100 ml. Can the hypothesis be accepted with a significance level of 5%?
1. State the null and alternative hypotheses:
H0 : μ = 20 mg/100 ml
H1 : μ ≠ 20 mg/100 ml
2. Calculate the limit of acceptance:
For a significance level of α = 0.05, the corresponding critical value is: zα/2 = 1.96.
Calculate the confidence interval for the mean:
3. Verify:
The value of the mean of the sample is:18.5.
4. Decide:
The nule hypothesis, H0, cannot be accepted with a significance level of 5%.
2)A company that packages peanuts states that at a maximum 6% of the peanut shells contain no nuts. At random, 300 peanuts were selected and 21 of them were empty.
1.With a significance level of 1%, can the statement made by the company be accepted?
2.With the same sample percentage of empty nuts and 1 − α = 0.95, what sample size would be needed to estimate the proportion of nuts with an error of less than 1%?
solution:
1A company that packages peanuts states that at a maximum 6% of the peanut shells contain no nuts. At random, 300 peanuts were selected and 21 of them were empty.
1.With a significance level of 1%, can the statement made by the company be accepted?
1. State the null and alternative hypotheses:
H0 : p ≤ 0.06
H1 : p > 0.06
2. Calculate the limit of acceptance:
α = 0.01 zα = 2.33.
Calculate the confidence interval for the proportion:
3. Verify:
4. Decide:
The nule hypothesis, H0, should be accepted with a significance level of 1%.
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Answer:
The nule speculation, H0, can not be frequent with a importance degree of five%.
The nule speculation, H0, have to be frequent with a importance degree of 1%.
Step- by -step explanation:
1)It is assumed that the common degree of prothrombin in a regular populace is 20 mg/a hundred ml of blood plasma with a trendy deviation of four miligramos/a hundred ml. To confirm this, a pattern is taken from forty people in whom the common is 18.five mg/a hundred ml. Can the speculation be frequent with a importance degree of five%?
solution:
It is assumed that the common degree of prothrombin in a regular populace is 20 mg/a hundred ml of blood plasma with a trendy deviation of four miligramos/a hundred ml. To confirm this, a pattern is taken from forty people in whom the common is 18.five mg/a hundred ml. Can the speculation be frequent with a importance degree of five%?
1. State the null and opportunity hypotheses:
H0 : μ = 20 mg/a hundred ml
H1 : μ ≠ 20 mg/a hundred ml
2. Calculate the restrict of acceptance:
For a importance degree of α = 0.05, the corresponding essential price is: zα/2 = 1.96.
Calculate the self belief c programming language for the suggest:
three. Verify:
The price of the suggest of the pattern is:18.five.
four. Decide:
The nule speculation, H0, can not be frequent with a importance degree of five%.
2)A enterprise that programs peanuts states that at a most 6% of the peanut shells incorporate no nuts. At random, three hundred peanuts have been decided on and 21 of them have been empty.
1.With a importance degree of 1%, can the announcement made with the aid of using the enterprise be frequent?
2.With the identical pattern percent of empty nuts and 1 − α = 0.95, what pattern length might be had to estimate the percentage of nuts with an blunders of much less than 1%?
solution:
1A enterprise that programs peanuts states that at a most 6% of the peanut shells incorporate no nuts. At random, three hundred peanuts have been decided on and 21 of them have been empty.
1.With a importance degree of 1%, can the announcement made with the aid of using the enterprise be frequent?
1. State the null and opportunity hypotheses:
H0 : p ≤ 0.06
H1 : p > 0.06
2. Calculate the restrict of acceptance:
α = 0.01 zα = 2.33.
Calculate the self belief c programming language for the percentage:
three Decide:
The nule speculation, H0, have to be frequent with a importance degree of 1%.