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 >
5.11 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
- or
- 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 do not have enough evidence to reject the null hypothesis
- or
- Since p ≥ α we reject the null hypothesis and accept the alternative
- or
- Since p ≥ α we accept the null hypothesis
- or
- Since p ≥ α we do not have enough evidence to reject the alternative hypothesis
(b) Construct a 95% con dence 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.
- Yes, the results agree because the confidence interval contains numbers less than 5 years
- or
- No, the results disagree because 5 is contained within the confidence interval
- or
- No, the results disagree because the confidence interval contains numbers greater than 5 years
- or
- It is impossible to compare confidence intervals and hypothesis tests since they are different procedures
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