Mathematics, 20.08.2020 18:01 kashbaby

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

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Answer from: kalbaugh

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 $H_0= \mu \leq 10$ and $H_A=\mu 10$ .

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 $\mu$ = population mean

So, Null Hypothesis, H_0 : $\mu \leq 10$ {means that the population mean is less than or equal to 10}

Alternate Hypothesis, H_A : $\mu$ > 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. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ t_n_-_1

where, $\bar X$ = sample mean = 12

s = sample standard deviation = 3

n = sample of observations = 10

So, the test statistics = $\frac{12-10}{\frac{3}{\sqrt{10} } }$ ~ t_9

= 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.

Answer from: Quest

i dont know if you cant find a way its best to actually add all of them start from 105 tho

step-by-step explanation:

I’m not sure how to solve these type of problems

Answer from: Quest

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation:

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