Some boxes of a certain brand of breakfast cereal include a voucher for a free video rental inside the box. The company that makes the cereal claims that a voucher can be found in 20 percent of the boxes. However, based on their experiences eating this cereal at home, a group of students believes that the proportion of boxes with vouchers is less than 0.2. This group of students purchased 65 boxes of the cereal to investigate the company’s claim. The students found a total of 11 vouchers for free video rentals in the 65 boxes.   Suppose it is reasonable to assume that the 65 boxes purchased by the students are a random sample of all boxes of this cereal. Based on this sample, is there support for the students’ belief that the proportion of boxes with vouchers is less than 0.2 ? Provide statistical evidence to support your answer.

According to a retail​ organization, holiday shoppers spent an average of $935.58 over the Thanksgiving weekend in 2016. The accompanying data show the amount spent by a random sample of holiday shoppers during the same weekend in 2017. ​$1,029 ​$875 ​$969 ​$838 ​$825 ​$813   ​$962 ​$1,032 ​$990 ​$996 ​$921 ​$664   ​$1,013 ​$1,030 ​$979 ​$878         Complete parts a through c.   Test the hypothesis that shoppers spent less than an average of $935.58 over the Thanksgiving weekend in 2017 using α=0.05.

It is often useful for retailers to determine why their potential customers chose to visit their store. Possible reasons include advertising, advice from a friend, or previous experience. To determine the effect of full-page advertisements in the local newspaper, the owner of an electronic-equipment store asked  randomly selected people who visited the store whether they had seen the ad. He also determined whether the customers had bought anything, and if so, how much they spent. Among the respondents who saw the ad, 49 made an average purchase of $97.38 with a variance of $622. Among the respondents who did not see the ad, 21 made an average purchase of  $92.01 with a variance of $283.3. Can the owner conclude that customers who see the ad spend more than those who do not see the ad (among those who make a purchase) at 5% significance level?     Population:  One Two Multiple       Formula #: Answer  Hypothesis Null H0 : (μ, π, σ², μd, μ1 - μ2, π1- π2, σ₁²…

In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).   In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 37% with a margin of error of 2.5%. Describe the conclusion about p using an absolute value inequality.   . That lets you type in a vertical bar | to represent absolute values. Also, when you type in  <  and then =, the symbolic entry option will automatically convert that to  ≤ . In the same way, if you type in  >  and then =, the symbolic entry option will automatically convert that to  ≥.   Be sure to use decimal numbers in your answer (such as using 0.40 for 40%).