Can please answer the following question with show up all explanation using by hand thank you

1. A marketing researcher wants to estimate the mean savings ($) realized by shoppers who showroom. Showrooming is the practice of inspecting products in retail stores and then purchasing the products online at a lower price. A random sample of 100 shoppers who recently purchased a consumer electronics item online after making a visit to a retail store yielded a mean savings of $58. Assume that the population is normally distributed and the population standard deviation is known as $55.

a. Is there evidence that the population mean savings for all showroomers who purchased a consumer electronics item is different from $50? (Use a 0.05 level of significance).

b. Compute the p-value and interpret its meaning.

c. Construct a 95% confidence interval estimate of the population mean.

2. You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time from the current 25 minutes. A random sample of 12 orders using the new delivery process was collected with a sample mean of 29 minutes. Assume that the population is normally distributed and population standard deviation of 4 minutes.

a. Conduct a test whether there is evidence that the population mean delivery time is different from 25 minutes given = 0.10.

b. Compute the p-value and interpret its meaning.

c. Construct a 90% confidence interval estimate of the population mean.

3. A survey of nonprofit organizations showed that online fundraising has increased in the past year. Based on a random sample of 55 nonprofit organizations, the mean one-time gift donation in the past year was $75. Assume that the population is normally distributed, and the population standard deviation is known as $9.

a. If you test the null hypothesis at the 0.01 level of significance, is there evidence that the mean onetime gift donation is different than $70.

b. Compute the p-value and interpret its meaning.

c. Construct a 99% confidence interval estimate of the population mean.