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svetoff [14.1K]
3 years ago
15

A random sample of 64 bags of white cheddar popcorn weighed, on average, 5.23 ounces with a standard deviation of 0.24 ounce.

Mathematics
1 answer:
emmasim [6.3K]3 years ago
3 0

Answer:

We conclude that cheddar popcorn weighed less than 5.5 ounces.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ =5.5 ounces

Sample mean, \bar{x} = 5.23 ounces

Sample size, n = 64

Alpha, α = 0.05

Sample standard deviation, σ = 0.24 ounce.

First, we design the null and the alternate hypothesis

H_{0}: \mu = 5.5\text{ ounces}\\H_A: \mu < 5.5\text{ ounces}

We use One-tailed z test to perform this hypothesis.

Formula:

z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

Putting all the values, we have

z_{stat} = \displaystyle\frac{5.23 - 5.5}{\frac{0.24}{\sqrt{64}} } = -9

Now, z_{critical} \text{ at 0.05 level of significance } =-1.645

Since,  

z_{stat} < z_{critical}

We reject the null hypothesis and accept the alternate hypothesis. Thus, we conclude that cheddar popcorn weighed less than 5.5 ounces.

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