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Answer:
Null Hypothesis, : p = 47%
Alternate Hypothesis, : p
47%
Step-by-step explanation:
We are given that in the last mayoral election in a large city, 47% of the adults over the age of 65 voted Republican.
A researcher wishes to determine if the proportion of adults over the age of 65 in the city who plan to vote Republican in the next mayoral election has changed.
<u><em>Let p = proportion of the population of all adults over the age of 65 in the city that plan to vote Republican in the next mayoral election.</em></u>
So, Null Hypothesis, : p = 47%
Alternate Hypothesis, : p
47%
Here, <u>null hypothesis states that</u> the proportion of adults over the age of 65 in the city who plan to vote Republican in the next mayoral election is equal to 47%.
On the other hand, <u>alternate hypothesis states that</u> the proportion of adults over the age of 65 in the city who plan to vote Republican in the next mayoral election is different from 47%.
Also, The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics;</u>
T.S. = ~ N(0,1)
Hence, the researcher should test the above null and alternative hypotheses.