Answer:
Based on the given data, it does not appear that the students are reasonably good at estimating one minute.
Explanation:
To determine if there is evidence to support the researcher's claim at the 1% significance level, we can perform a hypothesis test.
The null hypothesis (H0) assumes that the proportion of working students is still 66%, while the alternative hypothesis (H1) assumes that the proportion has changed.
Let's set up the hypotheses:
H0: p = 0.66 (proportion of working students is 66%)
H1: p ≠ 0.66 (proportion of working students has changed)
We can use the sample proportion, p, to test the hypotheses.
The sample proportion is calculated by dividing the number of working students by the total number of students surveyed.
In this case, the researcher surveyed 145 college students and found that 101 of them are working students.
Therefore, the sample proportion is:
p = 101/145 ≈ 0.6966
To perform the hypothesis test, we can use the z-test for proportions. The test statistic is calculated as:
z = (p - p) / sqrt(p(1-p)/n)
where p is the hypothesized proportion, p is the sample proportion, and n is the sample size.
Using the given values, we can calculate the test statistic:
z = (0.6966 - 0.66) / sqrt(0.66(1-0.66)/145)
≈ 1.47
At a 1% significance level, the critical z-value for a two-tailed test is approximately ±2.58.
Since the calculated test statistic (1.47) does not exceed the critical value of 2.58, we fail to reject the null hypothesis.
There is not enough evidence to support the researcher's claim that the proportion of working students has changed at the 1% significance level.
Therefore,
Based on the given data, it does not appear that the students are reasonably good at estimating one minute.