A random sample of 59 observations was selected from a normally distributed population. The sample mean was x = 95.1, and the sample variance was s2 = 35.2. Does this sample show sufficient reason to conclude that the population standard deviation is not equal to 8.2 at the 0.05 significance level? (a) State the appropriate null and alternative hypotheses. Ho: o ? v 8.2 Hạ: o? v 8.2 (ii) Find x*. (Give your answer correct to two decimal places.) (iii) Find the p-value. (Give your answer bounds exactly.)

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A random sample of 59 observations was selected from a normally distributed population. The sample mean was x =
95.1, and the sample
variance was s?
35.2. Does this sample show sufficient reason to conclude that the population standard deviation is not equal to 8.2 at
the 0.05 significance level?
(a) State the appropriate null and alternative hypotheses.
Ho: o ? v 8.2
Ha: o ? v8.2
(ii) Find x*. (Give your answer correct to two decimal places.)
(iii) Find the p-value. (Give your answer bounds exactly.)
< p <
(b) State the appropriate conclusion.
Reject the null hypothesis, there is not significant evidence that the population standard deviation differs from 8.2.
Reject the null hypothesis, there is significant evidence that the population standard deviation differs from 8.2.
Fail to reject the null hypothesis, there is not significant evidence that the population standard deviation differs from 8.2.
O Fail to reject the null hypothesis, there is significant evidence that the population standard deviation differs from 8.2.
Transcribed Image Text:A random sample of 59 observations was selected from a normally distributed population. The sample mean was x = 95.1, and the sample variance was s? 35.2. Does this sample show sufficient reason to conclude that the population standard deviation is not equal to 8.2 at the 0.05 significance level? (a) State the appropriate null and alternative hypotheses. Ho: o ? v 8.2 Ha: o ? v8.2 (ii) Find x*. (Give your answer correct to two decimal places.) (iii) Find the p-value. (Give your answer bounds exactly.) < p < (b) State the appropriate conclusion. Reject the null hypothesis, there is not significant evidence that the population standard deviation differs from 8.2. Reject the null hypothesis, there is significant evidence that the population standard deviation differs from 8.2. Fail to reject the null hypothesis, there is not significant evidence that the population standard deviation differs from 8.2. O Fail to reject the null hypothesis, there is significant evidence that the population standard deviation differs from 8.2.
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