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Complete Question:
The manager at a sports radio station will be covering several football games over the weekend. She knows that most of her listeners are at least 22 years old and wants to know what age group she should gear her advertisements to for the games. She takes a random sample of 46 listeners from age 22-39 and 57 listeners who are 40 and older and asks them if they are likely to tune in to football games. The "yes" responses are recorded in the file attached below.
1. At the 0.05 level of significance, is there a significant difference in the proportion of listeners based on age?
2. Is there evidence to suggest that there is a significant difference in the proportion of listeners based on age?
Answer:
1) There is no significant difference in the proportion of listeners based on age
2) No, there is no evidence
Step-by-step explanation:
Sample size of group 1,
Sample size of group 2,
Number of Yes in group 1,
Number of Yes in group 2,
Proportion of Yes in group 1:
Proportion of Yes in group 2:
Null Hypothesis,
Alternate Hypothesis,
Significance level,
Calculate the test statistic
Get the P-value from the probability distribution table:
At z = -1.54, P-value = 0.1236
Since (P-value = 0.1236) > (α = 0.05), we will accept the null hypothesis. This means that there is no evidence to suggest that there is difference in the proportion of listeners based on age.
