Use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance x, and sample sizes n, and n₂. Assume that the samples are independent, normal, and random. Answer parts (a) and (b). Ha: H1 H₂, α=0.05, n₁ = 17, n₂ = 8 (a) Find the critical value(s) assuming that the population variances are equal. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) (b) Find the critical value(s) assuming that the population variances are not equal. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)

There are two samples. Sample 1 has n=10 and a sample variance of 4. Sample 2 has n=8 and a sample variance of 9. Calculate the standard error of the difference between the two sample means (to 2 decimal points). Assume that the variances in the two populations that produced the samples are equal.

A researcher was interested in knowing if mean BMI was different between males and females. He obtained the following test results. Choose the correct interpretation of the results: F test p value = 0.30 Two sample t test, assume equal variance = 0.02 Two sample t test, assume unequal variance = 0.61 Mean BMI is not significantly different between males and females. None Mean BMI is higher in males than females. Mean BMI is significantly different between males and females.

Data on the weights (Ib) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. Diet Regular H2 nts 34 0.80711 lb 34 0.79119 lb 0.00432 lb 0.00747 lb 車 ent a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? bra O B. Ho H1 H2 Hq: Hy < H2 O A. Ho: H1 = H2 on! O D. Hg: H1 = H2 O C. Ho H H2 The test statistic, t, is (Round to two decimal places as needed.) The P-value is |. (Round to three decimal places as needed.) State the conclusion for the test. n oonr of diet soda have mean weights that are lower than the mean weight

Choose the appropriate statistical test. When computing, be sure to round each answer as indicated. A dentist wonders if depression affects ratings of tooth pain. In the general population, using a scale of 1-10 with higher values indicating more pain, the average pain rating for patients with toothaches is 6.8. A sample of 30 patients that show high levels of depression have an average pain rating of 7.1 (variance 0.8). What should the dentist determine? 1. Calculate the estimated standard error. (round to 3 decimals). [st.error] 2. What is thet-obtained? (round to 3 decimals). 3. What is the t-cv? (exact value) 4. What is your conclusion? Only type "Reject" or Retain"

​(a) Find the critical​ value(s) assuming that the population variances are equal. ​(b) Find the critical​ value(s) assuming that the population variances are not equal.

You have data drawn from a normal distribution with a known variance of 16. You set up the following NHST: • Ho: data follows a N(2, 4²) • HÃ: data follows a N(µ, 4²) where µ ‡ 2. Test statistic: standardized sample mean z. Significance level set to a = .05. You then collected n = 16 data points with sample mean 1.5. (a) Find the rejection region. Draw a graph indicating the null distribution and the rejection region. (b) Find the z-value and add it to your picture in part (a). (c) Find the p-value for this data and decide whether or not to reject Ho in favor of HA.

A researcher wants to measure average cardiovascular health of university students and compare those scores to the average scores in the general population. Assuming that population variance is known, what statistical test is most appropriate for this study?        independent-samples t-test     single-sample t-test     z-test for sample mean     related-samples t-test