For an inference about the difference between two population means #1-2, we know that if we have three assumptions: n₁ < 30 or n₂ < 30, normal populations and unknown population variance o2 = 0² = 0², then we will use a t-test statistic with pooled sample variance 7₁-1 n₁ + n₂ + 7₂-1 n₁+n₂-2
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- Students in one class are asked to complete the same questionnaire 3 times throughout the semester: at the beginning, at the midterm, and at the end. The purpose of the questionnaire is to track students' perception of their progress at different points in the semester. Scores at Time 1 (beginning of the semester), Time 2 (midterm), and Time 3 (end of semester) are compared against one another. What type of analysis of variance would be appropriate for examining the results from this dataset?We are running a hypothesis test to see if weight of African zebras is significantly different than that of Arabian horses. We assume weight in both populations is normally distributed and both populations have the same population variance in weight which is unknown to us, so we use the sample variances to estimate the standard error for our calculations. We have a sample of size 9 for the African zebras with mean 650 and a sample of size 16 for the Arabian horses with mean 660. If the pooled variance is 225, then what is the absolute value of the standardized test statistic for our data?4) We are running a hypothesis test to see if weight of African zebras is significantly different than that of Arabian horses. We assume weight in both populations is normally distributed and both populations have the same population variance in weight which is unknown to us, so we use the sample variances to estimate the standard error for our calculations. Our sampling has 8 African zebras and 6 Arabian horses. We find 3.01 as the absolute value of our standardized test statistic for our sample data. Is this data significant at the .02 level of significance? NONE OF THE OTHERS NO YES
- We are running a hypothesis test to see if blood pressure of African zebras differs significantly from Arabian horses. We assume blood pressure in both populations is normally distributed and both populations have the same population variance in blood pressure which is unknown to us, so we use the sample variances to estimate the standard error for our calculations. We have a sample of size 9 for the African zebras and a sample of size 16 for the Arabian horses. How many degrees of freedom does our test statistic have?Earlier this semester, we learned to use 2-Sample-TTest to compare the population means of two independent populations. One-way ANOVA is more powerful because it could compare the population means of three or more independent populations. However, use of one-way ANOVA also requires the assumption that the populations have the same variance. In this exercise, we will compare and contrast One-way ANOVA and 2-Sample-TTest. With the 2-Sample- TTEST, we will first choose 'No' for the pooled variances option, then re-run the test while choosing 'Yes' for the pooled variances option. Use the following data to complete these tasks. Depending on if you choose to do this by hand or using code, use the data format that suits you best - LONG form on top or WIDE form on bottom. Treatment One One One One One One One Two Two Two Two Two Two Two Treatment One 7.1 8.5 7.6 7.7 6.9 8.5 7.8 Response 7.1 8.5 7.6 7.7 6.9 8.5 7.8 1.4 4.1 4.3 3.9 4 4 4.6 p-value= Treatment Two 1.4 4.1 4.3 3.9 4 4 4.6 1. Use…We are running a hypothesis test to see if weight of African zebras differs significantly from that of Arabian horses. We assume weight in both populations is normally distributed and both populations have the same population variance in weight which is unknown to us, so we use the sample variances to estimate the standard error for our calculations. We have a sample size of 9 for the African zebras with mean 650 and a sample of size 16 for the Arabian horses with mean 658. If the pooled variance is 36, then what is the value of the standardized test statisitic for our data?
- A drug which is used for treating diabetes has potentially dangerous side effects if it is taken in doses which are larger than the required dosage for the treatment. A medical researcher believes that the variance in dosage is different for two tablets made by different production facilities. The sample variance of a sample of 11 dosages of tablet "A" is 0.013 . The sample variance of a sample of 28 dosages of tablet "B" is 0.01 . Construct the 90% confidence interval for the ratio of the population variances. Round your answers to four decimal places.Gestation period is the length of pregnancy, or to be more precise, the interval between fertilization and birth. In Syrian hamsters, the average gestation period is 16 days. Suppose you have a sample of 31 Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups, and who have an average gestation length of 17.1 days and a sample variance of 26.0 days. You want to test the hypothesis that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters. Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is sMM= a. 31, b. 0.5232, c. 0.7328, d. 0.9158. The t statistic is- a. 1.50, b. 2.10, c. 2.63, d. 1.20 Now suppose you have a larger sample size n = 95. Calculate the estimated standard error and the t statistic for this sample with the same sample average and the same…A study aims to compare the social media usage rates of men and women. Nine men and 9 women are drawn from the general population and the average time (in minutes) they spent on social media each day was compared (men’s mean = 40, sum of squares = 153; women’s mean = 48, sum of squares = 216). What is the (a) estimated population variance for each random sample, and (b) pooled variance? Estimated population variances = 19.13 and 27.00; Pooled variance = 23.07 Estimated population variances = 19.13 and 27.00; Pooled variance = 20.50 Estimated population variances = 17.00 and 24.00; Pooled variance = 20.50 Estimated population variances = 17.00 and 24.00; Pooled variance = 23.07
- 8 If the analysis of variance F-test leads to the conclusion that at least one of the model parameters is nonzero, can you conclude that the model is the best predictor for the dependent variable y? Can you conclude that all of the terms in the model are important for predicting y? What is the appropriate conclusion?We are running a hypothesis test to see if weight of African zebras is significantly different than that of Arabian horses. We assume weight in both populations is normally distributed and both populations have the same population variance in weight which is unknown to us, so we use the sample variances to estimate the standard error for our calculations. We have a sample of size 9 for the African zebras with mean 650 and a sample of size 16 for the Arabian horses with mean 659. If the pooled variance is 81, then what is the absolute value of the standardized test statistic for our data?A researcher decides to measure anxiety in group of bullies and a group of bystanders using a 23-item, 3 point anxiety scale. Assume scores on the anxiety scales are normally distributed and the variance among the group of bullies and bystanders are the same. A group of 30 bullies scores an average of 21.5 with a sample standard deviation of 10 on the anxiety scale. A group of 27 bystanders scored an average of 25.8 with a sample standard deviation of 8 on the anxiety scale. You do not have any presupposed assumptions whether bullies or bystanders will be more anxious so you formulate the null and alternative hypothesis based on that.
