A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation was 3. Using the .05 significance level: a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis

We conclude that the population mean is greater than 10.

Step-by-step explanation:

The complete question is: A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation was 3. Using the 0.05 significance level: a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis and .

We are given that a random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation was 3.

Let = population mean

So, Null Hypothesis, :    {means that the population mean is less than or equal to 10}

Alternate Hypothesis, : > 10    {means that the population mean is greater than 10}

The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                             T.S.  =    ~  

where, = sample mean = 12

             s = sample standard deviation = 3  

            n = sample of observations = 10

So, the test statistics =    ~  

                                    =  2.108  

The value of t-test statistics is 2.108.

Now, at a 0.05 level of significance, the t table gives a critical value of 1.833 at 9 degrees of freedom for the right-tailed test.

Since the value of our test statistics is more than the critical value of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the population mean is greater than 10.

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step-by-step explanation: