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pantera1 [17]
3 years ago
13

A sample of 16 items provides a sample standard deviation of 9.5. Test the following hypotheses using = .05. H0 : 2 50 Ha : 2 &g

t; 50 Calculate the value of the test statistic (to 2 decimals).
Mathematics
1 answer:
zavuch27 [327]3 years ago
3 0

Answer:

We conclude that the population standard deviation is greater than 50.

Step-by-step explanation:

We are given that a sample of 16 items provides a sample standard deviation of 9.5.

Let \sigma^{2} = <u><em>population standard deviation</em></u>

So, Null Hypothesis, H_0 : \sigma^{2} \leq 50     {means that the population standard deviation is less than or equal to 50}

Alternate Hypothesis, H_A : \sigma^{2} > 50      {means that the population standard deviation is greater than 50}

The test statistics that will be used here is <u>One-sample chi-square</u> test statistics;

                        T.S.  =  \frac{(n-1) \times s^{2} }{\sigma^{2} }  ~ \chi^{2}__n_-_1

where, s = sample standard deviation = 9.5

           n = sample of items = 16

So, <u><em>the test statistics</em></u> =  \frac{(16-1) \times 9.5^{2} }{50 }  ~ \chi^{2}__1_5

                                    =  27.08

The value of chi-square test statistics is 27.08.

Now, at 5% level of significance the chi-square table gives a critical value of 25.00 at 15 degrees of freedom for the right-tailed test.

Since the value of our test statistics is more than the critical value of chi as 27.08 > 25.00, so we have <u><em>sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.

Therefore, we conclude that the population standard deviation is greater than 50.

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