A hypothesis test is done in which the alternative hypothesis is that more than 10% of a population is left-handed. The p-value for the test is calculated to be 0.25. Which statement is correct

The p-value of a one-sided hypothesis test is 0.056. At the 10% significance level, what can we conclude if it was a two-sided hypothesis test instead?

If a school administrator claims that less than 50% of the students are dissatisfied with the food served in the school canteen. The claim used a sample data obtained from a survey of 500 students of the school wherein 54% indicated their dissatisfaction with the food served in the school canteen. Which of the following is the appropriate alternative hypothesis?p= 0.50p < 0.50p > 0.50p ≠ 0.50

Suppose that a major polling organization wanted to test the hypothesis that there was a change in the president’s “approval rating” since last month. Last month, 35% of the representative sample of registered voters approved of the president. For this month, the null hypothesis was that the approval rating equals 35% and the alternative hypothesis is that the approval rating does not equal 35%. The significance level for this test was 0.05.The results of the hypothesis test of the new survey showed a p-value of 0.008.Which of the following statements is correct? Check all that apply. The results were statistically significant. The results were not statistically significant. The null hypothesis should be rejected. The null hypothesis should be accepted. The null hypothesis cannot be rejected.

<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> ####

According to previous studies, 16% of the U.S. population is left-handed. Not knowing this, a high school student claims that the percentage of left-handed people in the U.S. is 15%.The student is going to take a random sample of 2100 people in the U.S. to try to gather evidence to support the claim. Let p be the proportion of left-handed people in the sample.Answer the following. (If necessary, consult a list of formulas.)(a)Find the mean of p.(b)Find the standard deviation of p.(c)Compute an approximation for P≥p0.15, which is the probability that there will be 15% or more left-handed people in the sample. Round your answer to four decimal places.