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Archy [21]
2 years ago
11

A random sample of 25 boxes of cereal have a mean of 372.5grams and a standard deviation of 15 grams. Does an average box of cer

eal contain more than 368 grams of cereal? Test hypothesis at the 5% significance level, outline all steps involved. (9mks)​
Mathematics
1 answer:
ss7ja [257]2 years ago
6 0

Using the t-distribution, it is found that since the <u>test statistic is less than the critical value for the right-tailed test</u>, there is not enough evidence to conclude that an average box of cereal contain more than 368 grams of cereal.

At the null hypothesis, it is <u>tested if the average box of cereal does not contain more than 368 grams</u>, that is:

H_0: \mu \leq 368

At the alternative hypothesis, it is <u>tested if it contains</u>, that is:

H_1: \mu > 368

We have the <em>standard deviation for the sample</em>, hence, the t-distribution is used to solve this question.

The test statistic is given by:

t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}

The parameters are:

  • \overline{x} is the sample mean.
  • \mu is the value tested at the null hypothesis.
  • s is the standard deviation of the sample.
  • n is the sample size.

In this problem, the values of the <em>parameters </em>are: \overline{x} = 372.5, \mu = 368, s = 15, n = 25.

Hence, the value of the <em>test statistic</em> is:

t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}

t = \frac{372.5 - 368}{\frac{15}{\sqrt{25}}}

t = 1.5

The critical value for a <u>right-tailed test</u>, as we are testing if the mean is greater than a value, with a <u>significance level of 0.05,</u> with 25 -1 = <u>24 df</u>, is of t^{\ast} = 1.71.

Since the <u>test statistic is less than the critical value for the right-tailed test</u>, there is not enough evidence to conclude that an average box of cereal contain more than 368 grams of cereal.

You can learn more about the use of the t-distribution to test an hypothesis at brainly.com/question/13873630

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