# 1. Field tests if a low-calorie sport drink found that 80 of the 100 who tasted the beveragepreferred it to the regular higher-calorie drink. A break-even analysis indicated that the launch ofthis product will be profitable if the beverage is preferred by more than 75% of all customers.Should the company launch the product? Test at 0.05 level of significance.

Question
Step 1

Test whether there is enough evidence to conclude that the company should launch the product.

State the appropriate hypothesis:

Let P be the population proportion of customers who preferred the beverage to the regular higher-calorie drink.

A break even analysis claimed that the launch of the product is profitable if the beverage is preferred to the regular higher-calorie drink by more than 75% of all customers.

That is, the launch of product is profitable if P >0.75.

The researcher’s objective is to test, whether or not the population proportion of customers who preferred the beverage to the regular higher-calorie drink is greater than 0.75.

The hypotheses are given below:

Null hypothesis:

H0 : P ≤ 0.75

That is, the population proportion of customers who preferred the beverage to the regular higher-calorie drink is less than or equal to 0.75.

Alternative hypothesis:

Ha : P > 0.75 (Right tailed test)

That is, the population proportion of customers who preferred the beverage to the regular higher-calorie drink is greater than 0.75.

Step 2

Obtain the sample proportion:

It is given that among a sample of 100 customers who tasted the beverage, 80 customers preferred the beverage to the regular higher-calorie drink.

The number of customers sampled is n = 100.

The number of customers preferred the beverage to the regular higher-calorie drink in the sample is x = 80.

The sample proportion of customers who preferred the beverage to the regular higher-calorie drink is obtained as 0.8 from the calculation given below:

Step 3

Obtain the test statistic value:

The number of orders sampled is n = 100.

The sample proportion of customers who preferred the beverage to the regular higher-calorie drink is p-hat = 8.

The population proportion of customers who...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in