Question

ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. Suppose that a particular branch the population mean amount of money withdrawn from ATMs per customer transaction over the weekend is $160 with a population standard deviation of $30. If a random sample of 36 customer transactions indicates that the sample mean withdrawal amount is $175, is there enough evidence to believe that the population mean withdrawal amount is no longer $160? Use a 0.01 level of significance (i.e., 1% significance level).

(a) Yes
(b) No
(c) We don’t have enough information to decide

[Hypothesis testing using t-distribution: one tail test] Phone industry manager thinks that customer monthly cell phone bills have increased. It used to be $52 per month on average. The company wishes to test this claim. Suppose a sample of 64 bills indicates an average of $56.5 with a sample standard deviation of $17.2. Is there enough evidence to prove the claim that the monthly cell phone bills have increased above $52 at 1% significance level?

(a) Yes
(b) No
(c) We don’t have enough information to decide

[Hypothesis testing using t-distribution: one tail test] Historically a soft drink bottle contains 2 liters. A recent article complains that bottles actually contain less than 2 liters. To verify this claim a sample of 49 bottles is taken. The sample average is 1.976 liters with the sample standard deviation of 0.12 liters. Based on this sample, is there enough evidence to prove the claim that bottles actually contain less than 2 liters at 5% significance level?

(a) Yes
(b) No
(c) We don’t have enough information to decide

[Hypothesis testing using sampling distribution of proportion: one tail test] In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign, and believe that the promotional campaign actually increased the proportion of tourists visiting Rock City. Of the last 400 tourists, 320 visited Rock City. Is there sufficient evidence to prove the claim at 5% significance level?

(a) Yes
(b) No
(c) We don’t have enough information to decide

Answer 1

Here we have to test that

Ho :μ = 160

H, :μ< 160

Where

Mo = 160

Population standard deviation =

08 = 0

n =sample size = 36

Sample mean =

T= 175

Here population standard deviation is known so we use z test.

Test statistic:

Τ – μο σίνη

175 – 160 30/36

$z=\frac{15}{5}$

z = 3

Test statistic = 3

alpha = 0.01

Test is one tailed (left tailed)test.

P value = P(z < 3)

             = 0.9987            (From statistical table of z values)

P value = 0.9987

Here p value > alpha

So we do not reject H0.

Conclusion There is not sufficient evidence to believe that the population mean withdrawal amount is no longer $160.

Answer: No