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5.11 Play the piano: Georgianna claims that in a small city renowned for its music school, the average child takes at least 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 using a hypothesis test.
The hypotheses for the test are:

Ho: μ = 5
Ha: μ > 5
Ho: μ = 5
Ha: μ < 5
Ho: μ = 5
Ha: μ ≠ 5

To execute this hypothesis test we should use a:

T-Test
Z-test

There are degrees of freedom for this test.
The test statistic is: (please round to two decimal places)
The p-value for this hypothesis test is: (please round to four decimal places)
The conclusion for the hypothesis test is:

Since p ≥ α we reject the null hypothesis and accept the alternative
Since p ≥ α we do not have enough evidence to reject the alternative hypothesis
Since p ≥ α we do not have enough evidence to reject the null hypothesis
Since p ≥ α we accept the null hypothesis

(b) Construct a 95% condence interval for the number of years students in this city take piano lessons, and interpret it in context of the data.
We are % confident that the true population mean years of piano lessons taken by the average child in this small town is between years and year. (please round to one decimal place)

(c) Do your results from the hypothesis test and the confidence interval agree? Explain your reasoning.

It is impossible to compare confidence intervals and hypothesis tests since they are different procedures
No, the results disagree because the confidence interval contains numbers greater than 5 years
No, the results disagree because 5 is contained within the confidence interval
Yes, the results agree because the confidence interval contains numbers less than 5 years

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