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

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.

H0: µ=2.55 H1: µ 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 µ and .

H0: µ=0.0105 H1: µ > 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.

H0: µ=75 H1: µ > 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) We will use T distribution because the normality assumption is satisfied and population standard deviation is unknown

b) We will use Non nonparametric method because the population standard deviation is unknown and normality assumption is not satisfied and sample size is less than 30

c) We will use Z distribution because the population standard deviation is known and normality assumption is satisfied

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