Suppose Heather suspects that the A string on her guitar is too sharp. She knows

Question

Suppose Heather suspects that the A string on her guitar is too sharp. She knows that playing an A2 note should produce a frequency of 110.00 Hz, and if the frequency is higher than that, the note is sharp. Because of slight variations in her guitar tuner's measurements, she played an A2 on the A string 10 times and recorded each of the measured frequencies. Heather found that her 10 measurements yielded a sample mean of 110.17 Hz and a sample standard deviation of 0.41 Hz. She then used this information to conduct a one-sample t-test of the null hypothesis Ho: 110.00 against the alternative hypothesis H1: > 110.00, where is the mean frequency, in hertz, produced when she plays an A2 note before tuning her guitar. Heather calculated a test statistic of 1.31 and a p-value of 0.1111. If she is conducting her test at a significance level of 0.10, what is her conclusion? (,-[om ) The decision is to fail to reject the null hypothesis at significance level = 0.10 . There is insufficient evidence that the mean frequency for all A2 notes played before tuning is more than 10.0 Hz.

Explanation / Answer

Since p-value os 0.1111>0.10,

So the decision is to Fail to reject the null hypothesis at a significance level of 0.10,

So there is sufficient evidence that the mean frequency for all A2 notes played before tuning is equal to 110.0 Hz

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