Using a computer, Linda simulates the responses of a sample of 120 people, assuming that the information in Table 2 is correct. She gets the results shown in the table below. TABLE 3 Response Would...

Extracted text: Using a computer, Linda simulates the responses of a sample of 120 people, assuming that the information in Table 2 is correct. She gets the results shown in the table below. TABLE 3 Response Would Call Would Text 24 or under 12 32 Age 25 or over 36 40 (d) A chi-square test for independence is conducted using the results in Table 3. i. Calculate the p-value for this hypothesis test. ii. A 5% significance level will be used. Will the null hypothesis be rejected? Explain briefly. Linda now uses the computer to simulate 20 samples of 120 people each, assuming that the information in Table 2 is correct. She has the computer determine, for each sample, whether the null hypothesis would be rejected or not rejected. Her results are shown below. Sample Result of Hypothesis Test Reject H Do not reject H, Reject Ho Reject Ho Do not reject H, Do not reject Ho 1 3 4 5 6. Reject Ho Reject Ho Reject H Reject Ho Do not reject Ho Reject H Do not reject Họ Do not reject Ho Reject H Do not reject H Do not reject Họ Reject H Reject H, Reject H 8 10 11 12 13 14 15 16 17 18 19 20 (e) According to the results of these 20 simulated samples, what should be Linda's estimate of the probability that Ho will be rejected? In light of this probability, should Linda redesign the study? Explain your answer.


Extracted text: 6. A communications company is conducting research concerning cellphone use. A questionnaire will be created in which, along with answering other questions, participants will state their age and will answer the following question: "A friend is going to drive you to a social event. You need to contact the friend to arrange a time and a place to meet. Would you call your friend or would you send a text?" Linda, an employee of the company, is asked to conduct an initial survey using 120 participants. ASsume that the participants will be selected at random. The results of the survey will be written in a table such as the one shown below. (Each star will be replaced by the number of people in that category.) TABLE 1 Response Would Call Would Text 24 or under Age 25 or over A chi-square test for independence will then be performed. (a) Write the null and alternative hypotheses for this significance test. population of cellphone users for the It is suggested to Linda that the true proportions of four categories are as shown in the table below. TABLE 2 Response Would Text Would Call 24 or under 0.09 0.27 Age 25 or over 0.32 .032 (b) Assume that the information in Table 2 is correct and that a cellphone user will be selected at random. Are the events "24 or under" and "would call" independent? Explain your answer. Linda will estimate the probability that her survey will result in the nuil hypothesis being rejected, given that the information in Table 2 is correct. (c) Explain the relevance of this probability.