Question

The following statement appeared on a box of Tide laundry detergent : "Individuals packages of Tide may weigh slightly more or less than the marked weight due to normal variations incurred with high speed packaging machines, but each day's production of Tide will average slightly above the marked weight."

a. Explain in statistical terms what the statement means.

b. Describe in words hypothesis test for checking the statement.

c. Suppose that the marked weight is 76 ounces. State in words the null and alternative hypothesis for the hypothesis test. Express those hypothesis in statistical terminology.

Short answer

a). A particular package weight may weigh slightly differ from the marked weight. The mean weight of all packages produced on any specific day exceeds marked weight.

b).

The null hypothesis would be that the population mean weight for a specified day equals the marked weight.

The alternative hypothesis would be that the population mean weight for a specified day exceeds marked weight.

c).$$\begin{gathered} H_0:\mu =0.76oz. \\ {H}_a:\mu >0.76oz. \end{gathered}$$

Step-by-step solution

Step 1. Explanation (a).

A particular package weight may weigh slightly differ from the marked weight. The mean weight of all packages produced on any specific day exceeds marked weight. Hence Here the variable under consideration is the weight of a package of a Tide.

Step 2. Description (b).

The null hypothesis :

population mean weight for a specified day = the marked weight.

The alternative hypothesis :

population mean weight for a specified day > marked weight.

In statistical terminology, the null and alternative hypothesis are

$H_0:$The population mean weight for a specified day = the marked weight.

$H_a:$The population mean weight for a specified day > the marked weight.

Step 3. Statement (c).

The null hypothesis :

population mean weight for a specified day = the marked weight of 76 oz.

The alternative hypothesis :

population mean weight for a specified day > marked weight of 76 oz.

In statistical terminology, the null and alternative hypothesis are

$H_0:$The population mean weight for a specified day equals the marked weight.

localid="1651916348839" $H_0:\mu =76oz.$

$H_a:$The population mean weight for a specified day exceeds the marked weight.

localid="1651916356260" $H_a:\mu >76oz.$