Question

1. A recent study has found that 34.2 percent of individuals in the country of Latveria are this, the local government of a city in Latveria is considering sponsoring a healthy eating campaig However, budgets are tight and the local leaders decide that they will only fund the healthy eating campaign if there is convincing evidence that the city's obesity rate is greater than the national obesity rate. The local government decides to collect data from 200 residents of the city. A test of significance will be conducted at the a 0.01 level for the following hypotheses Нор-0342 Ha:p>0.342 where p is the proportion of residents who are obese. (A) Describe what a Type I and Type Il error would be in the context of this problem. Also describe what would be the consequences of making each type of error. (B) In order to obtain the sample of 200 individuals, the local government incentivizes participation in the study with a coupon for a free meal at a local fast food chain. Researchers randomly choose 200 of the people who use the coupon at the restaurant. The results are that 87 of the 200 participants are obese, resulting in a Pvalue of 0.00278 for the hypotheses above. If there were no issues regarding the data, what would the Pvalue of 0.00278 lead you to conclude? (C) What is main flaw in the data collection strategy described in part (B)? Explain why it is of concern.

Answer 1

Hypotheses are:

$H_{0}:\mu=34.2,H_{a}:\mu>34.2$

(a)

Type I error is the probability of rejecting the true null hypothesis. That is local government incorrectly conclude that city's obesity rate is greater than national obesity rate but actually it is not greater than 34.2 percent.

Consequences; Local government will fund the healthy eating campaign while it is not necessary.

Type II error is the probability of fail to reject the false null hypothesis. That is local government incorrectly conclude that city's obesity rate is not greater than national obesity rate but actually it is greater than 34.2 percent.

Consequences; Local government will not fund the healthy eating campaign while it is necessary.

(b)

Since p-value is less than 0.01 so we reject the null hypothesis.

(c)

Sample is not simple random sample so it may not represent the picture correctly