Question

In a small city renowned for its music school, claims that the average child takes at least 5 years of piano lessons. Georgianna, a board member, claims this number is too high. Using 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, evaluate Georgianna’s claim using a hypothesis test at a 0.10 level of significance. *Assume that the distribution of years of piano lessons is normally distributed.

(a) State the hypothesis.

(b) State the conclusion with work to support your conclusion. When a TI-80 series is used, include all functions and calculations.

Answer 1

Sample size = n = 20

Sample mean = = 4.6

Standard deviation = s = 2.2

a)

Claim:  The average child takes at least 5 years of piano lessons.

The null and alternative hypothesis is

Level of significance = 0.10

b)

Here population standard deviation is unknown so we have to use t-test statistic.
Test statistic is

Degrees of freedom = n - 1 = 20 - 1 = 19

P-value = P(T < - 0.81) = 0.2131

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Now lets find the test statistic and p-value using TI-84 calculator.

Click on STAT ---------> TESTS ------> Stats ------->

: 5

: 4.6

Sx: 2.2

n: 20

Calculate

We get

Test statistic = - 0.81

P-value = 0.2131

P-value > 0.10 we fail to reject null hypothesis.

Conclusion:

The average child takes at least 5 years of piano lessons.

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Any doubt please comment!