STAT 218 Exam 1 review

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Feb 20, 2024

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Exam Review 1 Fall 2021 Total score: 76 1. Identify which of the variables are categorical and which are quantitative. (1 each) a.Researchers asked 200 people in Memorial Stadium if they were cheering for the Huskers. categorical b.Ford did a study on their trucks to examine the miles per gallon each car received on the highway. quantitative c.Researchers asked 143 random people in New York if they have taken a Cab in the past week. Categorical 2.Define a statistic in the context of the class. Where does its value come from? (2+1) A number summarizing the results in a sample. The value comes from the long run proportion 3.State True or False (1 each) a.The larger the p-value gets, the stronger the evidence against the null hypothesis

false b.It is always appropriate to use a standardized statistic to assess the significance of data, regardless of the sample size. true 4.*Extra Credit* If I were to stand outside of the Student Union during peak hours and ask students who were leaving various questions about the campus, what kind of sampling would I be doing? (1 pt) a.Simple Random Sampling b. Timed Population Sampling c.Targeted Density Sampling d.Convenience Sampling What is the issue with this kind of sampling? (1 pt) You only may get people who want to participate, and you may not get a good representation

5. What is a Random Sampling? List the benefits of Random Sampling. (2+1) Representative sample, it limits bias 6. The National Institutes of Health (NIH) is exploring the effect of a public service campaign aimed at addressing smart phone addiction. Before the campaign, it was estimated the Americans were spending 15.5 hours per week on their smart phone. Investigators hope that the campaign has reduced this figure. A sample of 61 Americans revealed that they spent an average of 13.5 hours per week on their smart phone, with a standard deviation of 6.8. Is there evidence that the campaign is working? (a) What are the observational units? (1 pt) Americans (b) Write the null and alternative hypotheses in words and in symbols (4 pts) H 0 : u = 15.5 H a : u < 15.5 Null: the long run average of Americans weekly usage of smart phones is 15.5 hours

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Alternative: the long run average of Americans weekly usage of smart phones is less than 15.5 hours (c) What is the parameter of interest (in words) and what is the statistic (value) (2 pts)? Parameter: long run average time (hours) Americans spend on their smart phones Stat: 13.5 hours (d) Compute a standardized statistic (BY HAND) and use the applet to confirm your calculation. (4 pts) t = 13.5 − 15.5 6.8 √ 61 =− 2.30 (e) Based on the standardized statistic and/or p-value, make A DECISION

(Regarding the null hypothesis) and A CONCLUSION for a general reader. (2 pts) Fail to reject the null hypothesis because p- value < .05 Americans use their phone less than 15.5 hours a day on a long run average (f) Calculate a 95% confidence interval and interpret it. (4+2) 13.5 ± 2 × 6.8 √ 61 13.5 ± 1.742 (11.758, 15.242) The true average time Americans spend on their phone falls between the interval (11.758, 15.242) (g) What is the Type I error in this scenario? Write its consequence. (2+2) Rejecting the null of Americans use their phones 15.5 hours a day, when it is true. There will be less campaigning, and it will not have the affect the investigators want. (h) What is the Type II error in this scenario? Write its consequence. (2+2)

Failing to reject the null of Americans use their phones 15.5 hours a day when it is false. There will be more campaigning when it is working well. 7. What is the symbol π ? What is the symbol ^ p ? Which one is a statistic, and which one is a parameter? (4 pt) π - long run proportion, parameter ^ p - sample proportion, statistic 8.What is the symbol μ ? What is the symbol x ? Which one is a statistic, and which one is a parameter? (4 pt) μ - population mean, parameter x - sample mean, statistic 9.For the following scenarios, write the null AND alternative hypothesis in words and in symbols ( 4 pts each ) a.For a professional dancer auditioning for a performance, it takes them an average of 4.5 minutes to learn the choreography. Faster Than U Studio claims that their

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dancers are of a higher class, and they learn the choreography quicker. H 0 : u = 4.5 H a : u < 4.5 Null: the long run average time it takes dancers to learn a dance is 4.5 minutes Alternative: the long run average time it takes dancers to learn a dance is less than 4.5 b.An entomologist is testing a pesticide that is much cheaper than anything on the market. In order to be effective in population control, the pesticide must kill about 50% of the bugs in the treatment area. H 0 : ^ p = 50% H a : ^ p > 50% Null: the long run proportion of the effectiveness of a pesticide is 50% Alternative: the long run proportion of the effectiveness of a pesticide is less than 50% 10. Time published a mobility study on the use of cellular devices. They found that 28 percent of people prefer to communicate over text messages as opposed to other

forms of communication. Researchers since believe that the number of people who prefer text messaging has increased. A random sample of 35 people was taken, and 19 said they preferred texting. (a) What are the observational units? ( 1 pt) Use of cellular devices (b) Write the null and alternative hypotheses in words and in symbols ( 4 pts ) H 0 : ^ p = 28% H a : ^ p > 28% Null: the long run proportion of people who prefer texting is 28% Alternative: the long run proportion of people who prefer texting is greater than 28% (c) What is the parameter of interest (in words), and what is the statistic (value) ( 2 pts )

Parameter: long run proportion of people who prefer to use text messages Stat: 54% (d) The applet values below are INCORRECT for analyzing the study above. Input a value for: sample size, a reasonable number of samples to run the analysis, and fill in the correct number for the “As extreme as” box on the bottom (change the sign if necessary). ( 1 pt each ) Sample size: 35 Number of samples: 100 As extreme as > 28% (e) The simulation was run with the correct values. The results are on the right. Identify the p-value. ( 1pt ) p-value= .486 (f) Make a decision regarding the null hypothesis given the p- value. ( 1pt )

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Reject the null because the p-value>.05 (g) The equation for the standardized statistic: z = statistic − hypothesized value Standard Error . Input the correct values and solve for the z-score ( 1pt ) z = 54% − 28% .084 √ 35 = -.023 (h) Make a conclusion. (remember the context!) ( 2pts ) People who prefer to communicate via text messaging has increased above 28% (i) Calculate a 95% confidence interval and interpret it. (4+2) 54 ± 2 × .014 ( 53.972 , 54.028 ) The true proportion of people who prefer to communicate via texting is between the interval ( 53.972 , 54.028 ) .

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