At the 0.05 level of​ significance, is there evidence of a difference among the age groups in the proportion of smartphone owners who have reached the maximum amount of data they are allowed to use as part of their​ plan, at least on​ occasion?   State the null and alternative hypotheses.      A. H0: π1=π2=π3=π4=0 H1: At least one of the πj is not equal to zero (where j=1, 2, 3, 4)   B. H0: π1=π2=π3=π4 H1: π1≠π2≠π3≠π4   C. ​Ho: P1=P2=P3=P4 ​H1: not all​ P's are equal   D. H0: π1=π2=π3=π4=0 H1: π1≠π2≠π3≠π4≠0   The test statistic is χ2STAT= ____  ​(Round to three decimal places as​ needed.)   p-value=____    __A__ H0. P-value is less than α... There __B__ significant evidence of a difference among the age groups in the proportion of smartphone owners who have reached the maximum amount of data they are allowed to use as part of their​ plan, at least on occasion.   What does the p-value mean? Choose the correct answer below.     A. The​ p-value is the probability of rejecting the null hypothesis if the test were repeated for different samples.   B. The​ p-value is the probability of falsely rejecting the null hypothesis.   C. The​ p-value is the probability that the null hypothesis is true.   D. The​ p-value is the probability of obtaining a result at least as extreme as the one obtained with this sample given that the null hypothesis is true.

Executives at The Thinking Channel have decided to test whether the educational backgrounds of the channel's viewers are different from the educational backgrounds of American adults (ages 25  and over) as a whole. The executives have the following information on the American adult population as a whole, obtained from a recent U.S. Current Population Survey.   Highest degree earned Less than high school High school College Higher than college Percent of population 12% 25% 55% 8% The executives also obtained data (from telephone surveys) on highest degrees earned for a random sample of 180  American adults who are Thinking Channel viewers. These data are summarized by the first row of numbers in the table below. These numbers are the frequencies for the degree categories that were observed in the sample of  180 . The second row of numbers gives the expected frequencies under the assumption that the distribution of highest degrees earned by Thinking Channel…

The following information comes from a study that examines changes in smoking status over a two-year period. In 2018, a sample of 70 adults over the age of 18 were asked to identify themselves as smokers or non-smokers. In 2020, the same 70 individuals were again be asked whether they were currently smokers or non-smokers.   2018 2020 Non-Smokers Smokers Non-Smokers 25 10 smokers 20 15   Describe the contingency table. Which statistical test is appropriate to use on these data?

Social media provides an enormous amount of data about the activities and habits of people using social platforms like Face book and Twitter. The belief is that mining that data provides a treasure trove for those who seek to quantify and predict future human behavior. A marketer is planning a survey of Internet users in the United States to determine social media usage. The objective of the survey is to gain insight on these three items: key social media platforms used, frequency of social media usage, and demographics of key social media platform users. a. For each of the three items listed, indicate whether the variables are categorical or numerical. If a variable is numerical, is it dis crete or continuous? b. Develop five categorical questions for the survey. c. Develop five numerical questions for the survey.