Chapter 19, Problem 1E

Parameters and hypotheses For each of the following situations, define the parameter (proportion or mean) and write the null and alternative hypotheses in terms of parameter values. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = the proportion of up days. H₀: p = 0.5 vs. H_A: p ≠ 0.5.

1. a) A casino wants to know if their slot machine really delivers the 1 in 100 win rate that it claims.
2. b) Last year, customers spent an average of $35.32 per visit to the company’s website. Based on a random sample of purchases this year, the company wants to know if the mean this year has changed.
3. c) A pharmaceutical company wonders if their new drug has a cure rate different from the 30% reported by the placebo.
4. d) A bank wants to know if the percentage of customers using their website has changed from the 40% that used it before their system crashed last week.

To determine

Define the parameter.

State the null and alternative hypotheses.

Answer to Problem 1E

The parameter is p, which is defined as the probability of winning on a slot machine.

The test hypotheses are given below:

Null hypothesis:$\underset{\_}{H_0:p=0.01}$

Alternative hypothesis:$\underset{\_}{H_A:p\ne 0.01}$

Explanation of Solution

Justification:

Parameter:

Any statistical measure based on all units in the population is called Parameter.

The study based on the casino wants to identify the probability of winning on a slot machine.

In the given situation, the parameter of interest is p, which is defined as the probability of winning on a slot machine.

Hypotheses:

The test hypotheses are given below:

Null hypothesis:

$H_0:p=0.01$

That is, the proportion of winning on a slot machine is 0.01

Alternative hypothesis:

$H_A:p\ne 0.01$

That is, the proportion of winning on a slot machine is different from 0.01.

To determine

Define the parameter.

State null and alternative hypothesis.

Answer to Problem 1E

The parameter is $\mu$, which is defined as the average amount spent on purchase per customer in a year.

The test hypotheses are:

Null hypothesis: $\underset{\_}{H_0:\mu =\$35.32}$

Alternative hypothesis: $\underset{\_}{H_A:\mu \ne \$35.32}$

Explanation of Solution

Justification:

The data represents the amount spent on purchase by the customer.

In the given situation, the parameter of interest is $\mu$, which is defined as the  average amount spent on purchase per customer in a year.

The test hypotheses are given below:

Null hypothesis: $\underset{\_}{H_0:\mu =\$35.32}$

That is, the average amount spent on purchase per customer in a year is $35.32.

Alternative hypothesis: $\underset{\_}{H_A:\mu \ne \$35.32}$

That is, the average amount spent on purchase per customer in a year is different from $35.32.

To determine

Define the parameter.

State null and alternative hypothesis.

Answer to Problem 1E

The parameter is p, which is defined as the percentage of patients cured by new drug.

The test hypotheses are given below:

Null hypothesis: $\underset{\_}{H_0:p=0.30}$

Alternative hypothesis: $\underset{\_}{H_A:p\ne 0.30}$

Explanation of Solution

Justification:

The data represents the effect of new drug on patients by pharmaceutical company.

In the given situation, the parameter of interest is p, which is defined as the percentage of patients cured by new drug.

The test hypotheses are given below:

Null hypothesis: $\underset{\_}{H_0:p=0.30}$

That is, the percentage of patients cured by new drug is 0.30.

Alternative hypothesis: $\underset{\_}{H_A:p\ne 0.30}$

That is, the percentage of patients cured by new drug is different from 0.30.

To determine

Define the parameter.

State null and alternative hypothesis.

Answer to Problem 1E

The parameter is p, which is defined as the percentage of Customers using the website of bank.

The test hypotheses are given below:

Null hypothesis: $\underset{\_}{H_0:p=0.40}$

Alternative hypothesis: $\underset{\_}{H_A:p\ne 0.40}$

Explanation of Solution

Justification:

A bank wants to identify the proportion of customers using the bank’s website.

In the given situation, the parameter of interest is p, which is defined as the percentage of Customers using the website of bank.

The test hypotheses are given below:

Null hypothesis: $\underset{\_}{H_0:p=0.40}$

That is, the percentage of Customers using the website of bank is 40%.

Alternative hypothesis: $\underset{\_}{H_A:p\ne 0.40}$

That is, the percentage of Customers using the website of bank is different from 40%.