Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person randomly selected 100 checks and recorded the cents portions of those checks. The table below lists those cents portions categorized according to the indicated values. Use a 0.10 significance level to test the claim that the four categories are equally likely. The person expected that many checks for whole dollar amounts would result in a disproportionately high frequency for the first category, but do the results support that expectation? Cents portion of check Number 0-24 25-49 50-74 75-99 35 22 19 24

In studying the responses to questions on a multiple-choice test, the following sample data are obtained. At the a 0.05 significance level, test the claim that the responses occur with the same frequency. Ho: The responses to the questions occur with the same frequency. H₁: The responses to the questions do not occur with the same frequency. Observed Response Frequency Expected Frequency (0-E)2 E A 6 16.2 8 B 10 16.2 C 24 16.2 D 18 16.2 8 E 23 16.2 a. What is the X2 test-statistic for this data? Round to four decimal places. x²= b. What is the p-value? Round to four decimal places. p-value= c. What would be the conclusion of this hypothesis test? O Fail to reject the hull hypothesis. Reject the null hypothesis. d. What is the final conclusion? O There is sufficient evidence to conclude the test question responses occur with the same frequency. There is sufficient evidence to conclude the test question responses do not occur with the same frequency. O There is not sufficient evidence to…

The Bureau of Labor Statistics reports that the official unemployment rate for Black people was 10.4% and 4.7% for White people in February 2015. Select all correct answers for this question. O The samples of white and black people are independent. The explanatory variable is the unemployment rate. The response variable is the unemployment rate. The response variable is race.

The U.S. National Center for Health Statistics complies birth statistics and publishes the results in vital statistics of the United States. The Center has historically believed that the mean of all newborns in the U.S. has been no less than 6.95 pounds. A sample of babies is selected so that the center can revise its belief. The following birth weights, in pounds are recorded: 7.4, 6.0, 8.6, 4.5, 2.0, 7.9, 4.0, 2.6, 5.9, 7.3, 7.3, 7.0, 6.3, 8.1, 7.1, 7.3, 6.6, 5.2, 9.8, 8.0, 10.9, 6.5, 3.8, 5.0, 8.0 a). At 5% level of significance, do these data provide sufficient evidence to refute the Center’s belief? Your conclusion must be in terms of the P-Value as well as setting up a Rejection Region. You must show all necessary work. b). Which statistical distribution should be applied in this situation and why? Explain carefully.

Suppose a random sample of 800 athletes from the college are asked what their major is. The table below shows the results of the survey. Observed Frequencies of Majors from the Sample Observed Frequency Outcome Math/Science 256 Arts & Humanities 190 Business & Economics 153 Other 201 The distribution of majors at the college is shown in the second column of the table below. Fill in the expected frequencies. (Round to the nearest whole number). Frequencies of Majors at the College Expected Percent Outcome Expected Frequency Math/Science 18 Arts & Humanities 29 Business & Economics 25

Thirty randomly selected students were asked how many self- help books they have read in the last three years. Their responses are in the following frequency table.

Several studies showed that after eating a low-fat cereal for two meals a day​, subjects had lost some weight.A cereal companyfinanced this research. Identify what is wrong. Choose the correct answer below.     A. Since the research is composed of voluntary response​ samples, there may be key data points missing.   B. The data used in the studies is not reliable because it was not measured by the administrator.   C. It is questionable that the sponsor is a cereal company because this sponsor can be greatly affected by the conclusion.   D. It is not possible to take accurate measurements.