Question

In 1993, Consumer Reports gave the following prices for a sample of 19 cellular phones: 2. 499 279 669 550 207 600 399 100 235 467 249 200 235 489 300 299 200 200 249 (a) Assuming a Normally distributed population, test the hypothesis at the 5% level of significance that the population mean price for cellular phones at the time of this survey was less than $400. Assume further that σ = 157. (b) Find a 94% CI for the mean price of all cellular phones. (c) Find the probability of a Type I error in performing this test. (d) The true mean price of all cell phones in 1993 was µ1 = $354. Find the probability of a Type II error for this test.

Answer 1

a)

as test statistic is in rejection region; we reject null hypothesis

we have sufficient evidence to coclude that  population mean price for cellular phones at the time of this survey was less than $400.

b)

for 94 % CI value of z=				1.88
margin of error E=z*std error                            =				67.714
lower confidence bound=sample mean-margin of error=				270.496
Upper confidence bound=sample mean +margin of error=				405.924

c)

probability of a Type I error in performing this test =0.05

d)