Question

1.) 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 Suppose that a particular branch the population mean amount of money withdrawn from ATMs per customer transaction over the weekend is $160 with a population standard deviation of $30.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 26. [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

2.) [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

3.) [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

SOLUTION 1 A] (1) Null and Alternative HypothesesThe following null and alternative hypotheses need to be tested:

Ho: μ=160

Ha μ≠​160

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, and the critical value for a two-tailed test is zc​=2.58.

The rejection region for this two-tailed test is R={z:∣z∣>2.58}

(3) Test Statistics

The z-statistic is computed as follows:

4) Decision about the null hypothesis

Since it is observed that ∣z∣=3>zc​=2.58, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0027, and since p=0.0027<0.01, it is concluded that the null hypothesis is rejected.

(5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to believe that the population mean withdrawal amount is no longer $160, at the 0.01 significance level.

SOLUTION 1B] (1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 52

Ha: μ > 52

This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, and the critical value for a right-tailed test is tc​=2.387.

The rejection region for this right-tailed test is R=t:t>2.387

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that t=2.093≤tc​=2.387, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value isp=0.0202, and since p=0.0202≥0.01, it is concluded that the null hypothesis is not rejected.

(5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to prove the claim that the monthly cell phone bills have increased above $52 at 1% significance level

NOTE: AS PER THE GUIDELINES I HAVE DONE THE FIRST QUESTION PLEASE RE POST THE REST. THANK YOU.