Answer:
We conclude that less than or equal to 50% of the student body supports him significantly.
Step-by-step explanation:
Mike, while campaigning for the student government presidency, is keen to determine if more than 50% of the student body supports him.
A random sample of 100 students was surveyed, with 55 expressing support for Mike.
Let p = the proportion of students backing Mike.
Thus, Null Hypothesis, : p
50% {indicating that the proportion of supporters among the student body is significantly less than or equal to 50%}
Alternate Hypothesis, : p > 50% {indicating that the proportion of supporters among the student body is significantly more than 50%}
The test statistics to be utilized here One-sample z proportion statistics;
T.S. = ~ N(0,1)
where, = the sampled proportion in favor of Mike =
= 0.55
n = number of sampled students = 100
Therefore, test statistics =
= 1.01
The z test statistic is 1.01.
At a significance level of 0.05, the z table provides a critical value of 1.645 for a right-tailed test.
Given that our test statistic falls below the critical value of z (1.01 < 1.645), we lack sufficient evidence to reject the null hypothesis as it remains outside the rejection region, leading to failure to reject our null hypothesis.
As a result, we conclude that less than or equal to 50% of the student body is in favor of him or the proportion supporting Mike is not significantly greater than 50%.