Determine for each scenario if you would use a normal (z) distribution, t- distr

Question

Determine for each scenario if you would use a normal (z) distribution, t- distribution, or if nonparametric methods must be used. Provide a simple explanation. (1 pt each)

(a) H0: =2.55 H1: 6= 2.55. Sample data: n=7, x=2.41, s=0.66. The sample data appear to come from a normally distributed population with unknown and .

(b) H0: =0.0105 H1: > 0.0105. Sample data: n=17, x=0.0134, s=0.0022. The sample data appear to come from a population with a distribution that is bimodal, and is unknown.

(c) H0: =75 H1: > 75. Sample data: n=15, x=66, s=12. The sample data appear to come from a normally distributed population with =14.

Explanation / Answer

(a) H0: =2.55 H1: 6= 2.55. Sample data: n=7, x=2.41, s=0.66. The sample data appear to come from a normally distributed population with unknown

Answer : t - distribution

(b) H0: =0.0105 H1: > 0.0105. Sample data: n=17, x=0.0134, s=0.0022. The sample data appear to come from a population with a distribution that is bimodal, and is unknown.

Answer : nonparametric distribution.

(c) H0: =75 H1: > 75. Sample data: n=15, x=66, s=12. The sample data appear to come from a normally distributed population with =14.

Answer : z - distribution.

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