Find the mean. You are given the following hypotheses:
H0 : µ = 60
HA : µ 6= 60
We know that the sample standard deviation is 8 and the sample size is 20. For what sample mean would the p-value be equal to 0.05? Assume that all conditions necessary for inference are satisfied.
t? vs. z?. For a given confidence level, t?df is larger than z?. Explain how t∗df being slightly larger than z∗ affects the width of the confidence interval.
Play the piano. Georgianna claims that in a small city renowned for its music school, the average child takes less than 5 years of piano lessons. We have a random sample of 20 children from the city, with a mean of 4.6 years of piano lessons and a standard deviation of 2.2 years.
(a) Evaluate Georgianna’s claim (or that the opposite might be true) using a hypothesis test.
(b) Construct a 95% confidence interval for the number of years students in this city take piano lessons, and interpret it in context of the data.
(c) Do your results from the hypothesis test and the confidence interval agree? Explain your reasoning.
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