Question

A software developer is in the process of estimating the average cost for its new mid-size projects in the coming year. while it is reasonable to assume that the average time taken to complete a project remains the same for the coming year, the cost (in dollars) incurred for a project should be calculated differently, and is given by 10000 1200x, where x is the number of days taken to complete the project. a sample of 35 past mid-size projects is taken. it is found that the mean and standard deviation of project completion time for this sample are, respectively, 27.2 days and 5.5 days. furthermore, 15 of these projects used visual basic as the main tool of the project.

a. i) at 5% significance level, is there any evidence that the proportion of projects using visual basic as the main tool is different from 0.25? justify your answer.
ii) calculate the p-value of the test statistic.
b. i) at 5% significance level, is there any evidence that the mean cost for the mid size projects will exceed $40000 in the coming year? justify your answer.
ii) calculate the p-value of the test statistic.

Answer 1

The null hypothesis (H0) states that the mean length of time is equal to or less than 2.5 hours, while the alternative hypothesis (Ha) states that the mean length of time is greater than 2.5 hours.

Step-by-step explanation:

To conduct a hypothesis test to determine if the mean length of time doing homework each week has increased, we can set up the null and alternative hypotheses. The null hypothesis (H0) states that the mean length of time is equal to or less than 2.5 hours, while the alternative hypothesis (Ha) states that the mean length of time is greater than 2.5 hours.

The null and alternative hypotheses can be written as:

H0: μ ≤ 2.5

Ha: μ > 2.5

Where μ represents the population mean.