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In order to conduct a hypothesis test for the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 4.8 and 0.8, respectively. (You may find it useful to reference the appropriate table: z table or t table) H0 : μ s 4 , 5 against HA: μ > 4 . 5 a-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic 1.837 a-2. Find the p-value. p-value<0.01 0.01 s p-value<0.025 0.025 s p-value<0.05 0.05 s p-value<0.10 p-value 0.10a-3. At the 5% significance level, what is the conclusion? 0 Reject H0 since the p-value is less than a. OReject Ho since the p-value is greater than a. Do not reject Ho since the p-value is less than a Do not reject Ho since the p-value is greater than a. a-4. Interpret the results at α-0.05. We conclude that the population mean is greater than 4.5 We cannot conclude that the population mean is greater than 4.5. OWe conclude that the population mean differs from 4.5. We cannot conclude that the population mean differs from 4.5a-4. Interpret the results at a 0.05 We conclude that the population mean is greater than 4.5. We cannot conclude that the population mean is greater than 4.5. We conclude that the population mean differs from 4.5 We cannot conclude that the population mean differs from 4.5. Ho: μ- 4.5 against HA: μ 4.5 b-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic 1.837b-2. Find the p-value. Op-value0.01 0 0.01 sp-value < 0.025 0.025 s p-value<0.05 0.05 s p-value<0.10 p-value 2 0.10 b-3. At the 5% significance level, what is the conclusion? Reject Ho since the p-value is less than a Reject Ho since the pvalue is greater than a Do not reject Ho since the p-value is less than a Do not reject Ho since the p-value is greater than ab-4. Interpret the results at α-0.05. We conclude that the population mean is greater than 4.5. OWe cannot conclude that the population mean is greater than 4.5 We conclude that the population mean differs from 4.5 We cannot conclude that the population mean differs from 4.5

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Answer Date: 23/01/2019 To test the hypothesis is that the population mean is greater than 4.50 at 5% significance level The null and alternative hypothesis is, Ho:4.50 Hai μ> 4.50 a-1 The t-test statistics is, 4.80-4.50 0.80//24 = 1.837 The t-test statistics is 1.837a-2) The P-value for this test is, From the t distribution table, show the degree of freedom 23 (24-1) and t-test statistics is 1.837 and the p-value is between0,025 and 0.05. The P-value for this test is 0.025 P 0.05 a-3) Decision The conclusion is that the p-value in this context is less than 0.05, so the null hypothesis is rejected at 5% level of significance. a-4) There is suficient evidence to indicate that the population mean is greater than 4.50. The result is statistically significantTo test the hypothesis is that the population mean is differs from 4.50 at 5% significance level The null and alternative hypothesis is, Ho : μ = 4.50 H,: # 4.50 b-1) The t-test statistics is, 4.80 4.50 0.80/v24 = 1.837 The t-test statistics is 1.837 b-2)The P-value for this test is, From the t distribution table, show the degree of freedom 23 (24-1) and t-test statistics is 1.837 and the p-value is between 0.05 and 0.10. The P-value for this test is 0.0s < P0.10 b-3) Decisioin The conclusion is that the p-value in this context is higher than 0.05, so the null hypothesis is not rejected at 5% level of significance. b-4) There is insufficient evidence to indicate that the population mean is differs from 4.50 The result is not statistically significant.

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