According to a book published in 2011, 45% of the undergraduate students in the United States show almost no gain in learning in their first two years of college (Richard Arum et al., Academically Adrift, University of Chicago Press, Chicago, 2011). A recent sample of 1540 undergraduate students showed that this percentage is 37%. Can you reject the null hypothesis at a 2.5% significance level in favor of the alternative that the percentage of undergraduate students in the United States who show almost no gain in learning in their first two years of college is currently lower than 45%. Use both the p-value and the critical-value approaches. Round your answers for the observed value of z and the critical value of z to two decimal places, and the p-value to four decimal places. Zobserved = i p-value = i Critical value = Hence we can conclude that the percentage of undergraduate students in the U.S. who show almost no gain in learning in their fırst two years of college is currently v 45%.

Suppose we are interested in the relationship between individuals’ place of residence (rural versus urban) and their political affiliation (Republican versus Democrat).  A random sample of 100 individuals yields the following crosstabulation: Political Affiliation               Place of Residence                Republican       Democrat               Rural                                        21                        29               Urban                                       14                        36 a) In words, what is the null hypothesis to be tested?   b) Is the relationship between place of residence and political affiliation statistically significant at the .05 level? (Be sure to show the statistics that lead to your decision.)   c) Compute and interpret an appropriate measure of association for the relationship between these two variables.

Forbes reports that women in general trust recommendations from Pinterest more than recommendations from any other social network platform. But does trust in Pinterest differ by gender? The following sample data show the number of women and men who state in a recent survey that they trust recommendations made on Pinterest.     Sample Trust recommendations made on Pinterest Women 150 117 Men 170 102   We want to determine whether trust in Pinterest differ by gender. Formulate the null and the alternative hypotheses. Use 1 to represent women and 2 to represent men. H0: Ha:   Null: p1 – p2 ≥ 0; Alternative: p1 – p2 < 0 Null: p1 – p2 = 0 ; Alternative: p1 – p2 ≠ 0 Null: p1 – p2 ≤ 0; Alternative: p1 – p2 > 0   B. What the test statistics? You probably need to find the pooled proportion first.  Pooled proportion is  ___________.  0.6 0.78 0.6844   C. Test statistic is ________. 3.46 1.28 66.41 4.36

2. Several years ago, a census of all students enrolled at a large undergraduate university revealed that 19% of the students were seniors, 23% were juniors, 27% were sophomores, and 31% were freshmen. This year, the student senate did a survey to see whether these percentages have remained the same. A random sample of 200 students included 50 senior, 46 juniors, 55 sophomores, and 49 freshmen. Using a 2.5% significance level, test the null hypothesis that the percentages are still 19% seniors, 23% juniors, 27% sophomores, and 31% freshmen. Use the Critical Value Approach.

If sample data is such that for a one-tailed test of ? you can reject H0 at the 1% level of significance, can you always reject H0 for a two-tailed test at the same level of significance? Explain your answer?   A. Yes. If H0 for a one-tailed test is rejected at the 1% level of significance, it will always be rejected for a two-tailed test at the same level of significance. B. No. If H0 for a one-tailed test is rejected at the 1% level of significance, it will never be rejected for a two-tailed test at the same level of significance.     C. Yes. The P-value for the two-tailed test could be greater than 0.01. D. No. The P-value for the two-tailed test could be greater than 0.01.

A sociologist studying New York City ethnic groups wants to determine if there is a difference in income for immigrants from four different countries during their first year in the city. She obtained the data in the following table from a random sample of immigrants from these countries (incomes in thousands of dollars). Use a 0.05 level of significance to test the claim that there is no difference in the earnings of immigrants from the four different countries. Country I Country II Country III Country IV 12.3 8.3 20.4 17.3 9.1 17.2 16.5 8.7 10.9 19.2 22.8 14.2 8.8 10.2 5.5 21.4 16.1   19.2 19.3   (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Round your answers to three decimal places.) SSTOT =   SSBET =   SSW =   Find d.f.BET, d.f.W, MSBET, and MSW. (Round your answer to three decimal places for MSBET and MSW.) dfBET =   dfW =   MSBET =   MSW =   Find the value of the sample F statistic. (Round your answer to three decimal…

Medical researchers followed 6272 Swedish men for 30 years to see if there was any association between the amount of fish in their diet and prostate cancer. (“Fatty Fish Consumption and Risk of Prostate Cancer,” Lancet, June 2001).  A summary of the data is given in the table below.  Fish Consumption No Prostate Cancers Prostate Cancers Never/Seldom 110 14 Small part of diet 2420 201 Moderate part of diet 2769 209 Large part of diet 507 42   A) If a patient is randomly selected, what is the probability that he/she had prostate cancer given that fish was never or seldom a part of the diet?  Round your answer to three decimal places and include the leading zero. B) If a patient is randomly selected, what is the probability that s/he ate fish as a large part of their diet given that they had prostate cancer.  Round your answer to two decimal places and include the leading zero.

Answer the questions in the images.

The National Study of the Changing Work Force conducted a study of 2958 wage and salaried workers on issuesranging from relationships with their bosses to household chores. The data were gathered through hour-longtelephone interview with a nationally representive sample. In response to the questions “What does your job meanto you?” 1538 people responded that they “Receive personal satisfaction from success at work.” Let p be thepopulation proportion of people who receive personal satisfaction from success at work. (a) Find a 95% CI for the true value of p. (b) How large of sample is needed if we wish to be 99% confident that the sample proportion of p is within1% of the true population proportion.