T value and P value

Question

Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 75 students shows that 35 have jobs. Do the data indicate that more than 35% of the students have jobs? (Use a 5% level of significance.)

c) Use the sample test statistic to compute the corresponding distribution value. (Round your answer to two decimal places.)

d) Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer 1

We use a hypothesis test for a population proportion.

Null hypothesis p = 0.35

Alternative hypothesis p > 0.35

Test statistic for a proportion is:

where

p-hat is the sample proportion

p₀ is the hypothesized population proportion

n is sample size

From the problem:

p-hat is 35 / 75 = 0.4667

p₀ = 0.35

n = 75

Calculating the test statistic gives you z = 2.12.

Use a standard normal distribution table or calculator to find the p-value associated with z = 2.12. Since it's a one-tailed test, we're looking for the area of the curve to the right of z = 2.12. The corresponding p-value is 0.017.

c) The sample test statistic is 2.12 (rounded to two decimal places).

d) The p-value of the test statistic is 0.0170 (rounded to four decimal places)

Since the p-value (0.0170) is less than the significance level (α=0.05), we reject the null hypothesis. This suggests that there is sufficient evidence to support Dean Renata's claim that more than 35% of the students at Flora College have jobs.

Hope this was helpful.