SOLUTION: A random sample has 61 values. The sample mean is 9.9 and the sample standard deviation is 2. Use a level of significance of a=0.01 to conduct a right-tailed test of the claim tha

Question 930129: A random sample has 61 values. The sample mean is 9.9 and the sample standard deviation is 2. Use a level of significance of a=0.01 to conduct a right-tailed test of the claim that the population mean is 9.2 ( i.e, H_0: u= 9.2, H_1: u>9.2).
A)Compute the sample test statistic t.
B) Do we reject or fail to reject H_0? Explain you reasoning.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
A)

t = (xbar - mu)/(s/sqrt(n))
t = (9.9 - 9.2)/(2/sqrt(61))
t = 2.733587

The test statistic is approximately t = 2.733587

---------------------------------------------------------------
B)

Use a calculator or table to get

P(t > 2.733587) = 0.0041

Note: the degrees of freedom is df = n-1 = 61-1 = 60

So the p-value is 0.0041

Notice how the p-value (0.0041) is smaller than the significance level (alpha = 0.01), so we reject the null hypothesis H0. We reject H0 whenever (pvalue) < (alpha).

------------------------------------------------------------------------------------------------------------------------

If you need more one-on-one help, email me at jim_thompson5910@hotmail.com. You can ask me a few more questions for free, but afterwards, I would charge you ($2 a problem to have steps shown or $1 a problem for answer only).

Alternatively, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Any amount is greatly appreciated as it helps me a lot. This donation is to support free tutoring. Thank you.

Jim
------------------------------------------------------------------------------------------------------------------------
RELATED QUESTIONS
A random sample has 42 values. The sample mean is 9.5 and the sample standard deviation... (answered by ewatrrr)

A random sample has 42 values. The sample mean is 9.5 and the sample standard deviation... (answered by Boreal)

A random sample of 10 observations from one population revealed a sample mean of 23 and a (answered by stanbon)

random sample of 200 measurements give a mean of 50 and standard deviation of 9. at 5%... (answered by stanbon)

The mean I.Q of a sample of 1600 children was 99. Is it likely that this was a random... (answered by math_tutor2020)

. A random sample of 41 observations was selected from a normally distributed population. (answered by stanbon)

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of... (answered by ewatrrr)

The following information is available. H0: μ ≤ 25 H1: μ > 25 The... (answered by ewatrrr)

A random sample of 121 observations from a population with a standard deviation of 50... (answered by stanbon)