In carrying out a one-sample t-test for a mean, the hypotheses H0:mu=10 against HA:mu>10 were tested.A sample of size 21 was used, giving a t-statistic of 2.00.Determine the P-value associated with this test.

We conduct a test for a mean with a two-sided alternative hypothesis using a t-test. There were 30 observations in the sample and the calculated test statistic was 2.36, what is the appropriate p-value?

For a 1 Sample T test, when the sample size is 10, what type of distribution do we use to find the p-value?

(a) A statistician randomly sampled 100 observations and found X̄ = 106 and s = 35. Calculate the t statistic and p value for testing.     H0 : μ = 100 against HA : μ > 100.Carry out the test at the 1% level of significance.(b) Repeat part (a), with s = 25.(c) Repeat part (a), with s = 15.Repeat question 1 using HA : μ ≠ 100.

In a two-tailed hypothesis test situation, the test statistic is determined to be t = -2.032. The sample size is 35. The p-value for this test is-.05.+.05.-.10.+.10.

<p>a) To infer if the population mean is less than 100 at the 10% significance level, we can perform a one-sample t-test.</p> <p>Step 1: State the null hypothesis (H0) and the alternative hypothesis (H1). H0: μ = 100 (The population mean is equal to 100) H1: μ &lt; 100 (The population mean is less than 100)</p> <p>Step 2: Calculate the test statistic. The formula for the t statistic is:</p> <p>t = (x̄ - μ) / (s/√n)</p> <p>where x̄ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.</p> <p>t = (75 - 100) / (50/√8) = -1.414</p> <p>Step 3: Determine the critical value from the t-distribution table. For a one-tailed test at the 10% significance level with 7 degrees of freedom (n-1), the critical value is -1.415.</p> <p>Step 4: Compare the test statistic with the critical value. If the test statistic is less than the critical value, we reject the null hypothesis. In this case, -1.414 is greater than -1.415, so we do not reject the null hypothesis. Therefore, we cannot infer at the 10% significance level that the population mean is less than 100.</p> <p>b) If we know that the population standard deviation is 50, we can perform a z-test instead of a t-test.</p> <p>Step 1: The null and alternative hypotheses are the same as in part (a).</p> <p>Step 2: Calculate the z statistic using the formula:</p> <p>z = (x̄ - μ) / (σ/√n)</p> <p>where σ is the population standard deviation.</p> <p>z = (75 - 100) / (50/√8) = -1.414</p> <p>Step 3: Determine the critical value from the z-distribution table. For a one-tailed test at the 10% significance level, the critical value is -1.28.</p> <p>Step 4: Compare the z statistic with the critical value. In this case, -1.414 is less than -1.28, so we reject the null hypothesis. Therefore, we can infer at the 10% significance level that the population mean is less than 100.</p> <p>c) The test statistics differ because a t-test is used when the population standard deviation is unknown and is estimated from the sample, while a z-test is used when the population standard deviation is known. The t-distribution is wider and has heavier tails than the z-distribution, which leads to a larger critical value and a higher chance of not rejecting the null hypothesis.</p> ####