Question

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(1 point) 35 people are randomly selected and the accuracy of their wristwatches is checked, with positive errors representing watches that are ahead of the correct time and negative errors representing watches that are behind the correct time. The 35 values have a mean of 94sec and a standard deviation of 228 sec. Use a 0.02 significance level to test the claim that the population of all watches has a mean of Osec. The test statistic is The P-value is The final conclustion is A. There is sufficient evidence to warrant rejection of the claim that the mean is equal to 0 B. There is not sufficient evidence to warrant rejection of the claim that the mean is equal to 0
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Answer 1

We would be looking at the first set of questions here on hypothesis test as:

Q1) a) As we are testing here whether the population mean is 0, therefore the test statistic here is computed as:

$t^* = \frac{\bar X - \mu_0}{\frac{s}{\sqrt{n}}} = \frac{94 - 0}{\frac{228}{\sqrt{35}}} = 2.4391$

Therefore 2.4391 is the required test statistic value here.

b) As we are testing here whether the mean is 0, therefore this is a two tailed test and the p-value here is obtained as:
p = 2P( t₃₄ > 2.4391) = 2*0.01 = 0.02

Therefore 0.02 is the required p-value here.

c) As the p-value here is 0.02 = 0.02 which is the level of significance, therefore the test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here to reject the claim that the mean is equal to 0.