A random sample of 10 children found that their average growth for the first year was 9.8 inches, with a standard deviation of 0.96 inches. Find the 85% confidence interval of the mean growth of all American children in the first year of life. What is the name of the confidence interval? Two Independent Samples t Interval One Sample t Interval ANOVA One Proportion z Interval Two Proportion z Interval Correlation t Interval Chi-Square Interval for Independence One Sample z Interval Chi-Square Goodness of Fit Interval Paired Samples t Interval Have the assumptions been met? Check which assumptions have been met. Equal population variances Random sample Independent trials Normal Sampling Distribution: n₁p₁ ≥ 5, n₁(1 - p₁) ≥ 5 n₂p₂ ≥ 5 & n₂(1 - p₂) ≥ 5 Expected values ≥ 5 Known population standard deviation Fixed number of trials Normal Sampling Distribution: n ≥ 30 or Population is normally distributed Two outcomes Independent samples Unknown population standard deviation The proportion is constant Normal Sampling Distribution: np ≥ 5 & n(1 - p) ≥ 5 Check which assumptions have not been met so we would say "the assumption may not be met" or have to check the histogram, box plot, and normal quantile plot. The proportion is constant Expected values ≥ 5 Normal Sampling Distribution: np ≥ 5 & n(1 - p) ≥ 5 Equal population variances Normal Sampling Distribution: n ≥ 30 or Population is normally distributed Fixed number of trials Independent samples Normal Sampling Distribution: n₁p₁ ≥ 5, n₁(1 - p₁) ≥ 5 n₂p₂ ≥ 5 & n₂(1 - p₂) ≥ 5 Random sample Known population standard deviation Independent trials Unknown population standard deviation Two outcomes Which sample statistics are required? μ0 p0 p s2 σ x p^ s μ x¯ Fill in the interval rounding to three decimal places for each number. ____ < μ< _____

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...