In: Business and Management

Submitted By himanshujain316
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How to Construct a Confidence Interval
Instructions on the left Instructions on the right pertain to means pertain to proportions 1. POPULATION a. Identify the parameter of interest: π : proportion µ : Mean Numerical (Measurement) Categorical (success-failure) b. Describe the variable in context with the problem: µ = mean of the amount of drying time of a particular paint. π = proportion of people in the community who prefer smoking

2. STATISTICAL METHOD a. Determine the confidence level (1 - α) and the level of significance α . NOTE: If not specified, set the confidence to 0.95 (95%) and the level of significance to 0.05. b. Identify the required formula for the confidence interval: When σ known: ⎛ σ ⎞ x ± ( zcriticalvalue )⎜ ⎟ ⎜ ⎟ ⎝ n ⎠ p ± ( zcriticalvalue ) p (1 − p ) n When σ unknown: ⎛ s ⎞ x ± (tcriticalvalue )⎜ ⎟ ⎜ ⎟ ⎝ n⎠ 3. SAMPLE a. Calculate or identify the descriptive statistics: Descriptive statistics needed: • the sample mean • standard deviation • sample size b. Check the conditions for normality: population is normal OR n ≥ 30 Descriptive statistics needed: • the sample proportion • sample size

np ≥ 10 AND n(1 − p ) ≥ 10

Page 1 of 2

4. STATISTICAL RESULTS a. Find the required z or t critical value: z critical value: 1. Find


Same as z critical value information on the left.

2 2. Take this value and locate it in the standard normal probability table and identify the z critical value.
NOTE: Commonly used z critical value Confidence Level α 90% 95% 99% .10 .05 .01


.05 .025 .005

z critical value 1.645 1.960 2.576

t critical value: 1. Determine the degrees of freedom: df = (n - 1) 2. Use the appropriate confidence level and the df and locate the t critical value in the t critical value table. For example, Confidence Level 90% 98% 95% df 15 7 23 t critical value 1.75 3.00 2.07

b. Compute the…...

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