Is the statement Ho: 14 = 6 a valid null hypothesis? O No, equalities are not permitted in the null hypothesis. O Yes, this is a statement that compares a parameter to a value. O No, there is no parameter. O Yes, this is a statement that compares 2 values.
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- A Bitter Dispute With the publication of Ars Magna, a dispute intensified between Jerome Cardan and another mathematician named Niceolo Fontana, otherwise known as Tartaglia. What was the dispute, and how did it arise? In your opinion, who was at fault? Write a paragraph or two about your findings.Is the statement Ho: 14 = 6 a valid null hypothesis? Yes, this is a statement that compares a parameter to a value. Yes, this is a statement that compares 2 values. No, there is no parameter. No, equalities are not permitted in the null hypothesis.Some of the statements below refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the appropriate parameter (μ or p). Part 1)About half of Americans prefer to live away from cities, given the choice. a)H0: p ≤ 0.50, Ha: p > 0.50 b)H0: μ = 0.5, Ha: μ ≠ 0.5 c)H0: μ ≠ 0.5, Ha: μ = 0.5 d)H0: p = 0.50, Ha: p ≠ 0.50 e)H0: p ≠ 0.50, Ha: p = 0.50 f)H0: μ ≥ 0.5, Ha: μ < 0.5 g)H0: p ≥ 0.50, Ha: p < 0.50 h)H0: μ ≤ 0.5, Ha: μ > 0.5 Part 2) Europeans have a mean paid vacation each year of six weeks. a) H0: p ≥ 6, Ha: p < 6 b) H0: μ ≥ 6, Ha: μ < 6 c) H0: p = 6, Ha: p ≠ 6 d) H0: μ ≠ 6, Ha: μ = 6 e) H0: μ = 6, Ha: μ ≠ 6 f) H0: p ≠ 6, Ha: p = 6 g) H0: p ≤ 6, Ha: p > 6 h) H0: μ ≤ 6, Ha: μ > 6 Part 3) The chance of developing breast cancer is under 11% for women. a) H0: μ < 11, Ha: μ ≥ 11 b) H0: μ ≥ 11, Ha: μ…
- Some of the statements below refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the appropriate parameter (μ or p) Part 1) About half of Americans prefer to live away from cities, given the choice. a) H0: p ≤ 0.50, Ha: p > 0.50 b) H0: μ = 1 2 , Ha: μ ≠ 1 2 c) H0: μ ≠ 1 2 , Ha: μ = 1 2 d) H0: p = 0.50, Ha: p ≠ 0.50 e) H0: p ≠ 0.50, Ha: p = 0.50 f) H0: μ ≥ 1 2 , Ha: μ < 1 2 g)H0: p ≥ 0.50, Ha: p < 0.50 h) H0: μ ≤ 1 2 , Ha: μ > 1 2 Part 2) Europeans have a mean paid vacation each year of six weeks. a) H0: p ≥ 6, Ha: p < 6 b) H0: μ ≥ 6, Ha: μ < 6 c) H0: p = 6, Ha: p ≠ 6 d) H0: μ ≠ 6, Ha: μ = 6 e) H0: μ = 6, Ha: μ ≠ 6 f) H0: p ≠ 6, Ha: p = 6 g) H0: p ≤ 6, Ha: p > 6 h) H0: μ ≤ 6, Ha: μ > 6Which of the following alternative hypotheses make a hypothesis test one-tailed? Select all that apply. 1 Parameter is less than a value 2 Parameter is greater than a value 3 Parameter is not equal to a valueWhich statement describes a Type II Error? Fail to reject the null hypothesis H0, when H0 is actually true Reject the null hypothesis H0, when H0 is actually true Fail to reject the null hypothesis H0, when H0H0 is false Reject the null hypothesis H0, when H0 is actually false
- f our null hypothesis is H0: ? = 40, what are the three possiblealternative hypotheses?The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested?A. H and 0 : μ ≥ 7 1.HO : μ < 7B. H and 0 : μ ≤ 5 1.HO : μ > 5C. H and 0 : σ ≤ 10 1.HO : σ > 10C. H and 0 : μ = 3 1.HO : μ ≠ 3D. H and 0 : σ = 8 1.HO : σ ≠ 8When is there a risk of a Type II error? a. The risk of a Type II error is independent from the decision about a hypothesis test b. whenever H0 is rejected c. whenever the decision is "do not reject H0" d. whenever H1 is rejected
- The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested? H and 0 : μ ≥ 7 1.HO : μ < 7 H and 0 : μ ≤ 5 1.HO : μ > 5 H and 0 : σ ≤ 10 1.HO : σ > 10 H and 0 : μ = 3 1.HO : μ ≠ 3 H and 0 : σ = 8 1.HO : σ ≠ 8Suppose an engineering firm is asked to check the safety of a dam. A) What kind of mistake would be made if the Ho (null hypothesis) that the dam is safe is wrongly rejected? B) What kind of mistake would be made if the Ho that the dam is safe is wrongly accepted?Express the null hypothesis H0 and the alternative hypothesis Ha in notation form in the following scenarios. 1. The mean annual income of workers who are college graduates is greater than Php100,000 a year. 2. The percentage of women who watches sports on TV is not 40% as claimed by a researcher