Consider a random sample of 11 observations, given in the following table, from

Question

Consider a random sample of 11 observations, given in the following table, from a normal population with hypothesized mean 57.87 .

a.Write the four parts for a one-sided, right-tailed hypothesis test concerning the population mean with  =0.005.  

Null hypothesis:

Alternative hypothesis:

Compute the sample mean, the sample standard deviation, and the value of the test statistic (Give your answers to three decimal places.):  
x=
S=
t=

Draw a conclusion about the population mean.

There is no evidence to suggest that the mean is greater than 57.87.

Find the  pvalue associated with this hypothesis test (Give your answer to three decimal places.):  
p=

Explanation / Answer

the standard deviation and the mean of the data points give

A) the null hypothesis = H0= u = 57.87

the alternate hypothesis = Ha = u>57.87

as alpha = 0.005

the degree of freedom = 11-1 = 10

the critical region = t>3.17

the test static = (59.62- 57.87)/(1.44/sqrt(11))

= 4.032

as the t static = 4.032>3.17 therefore we will reject the null hypothesis.

the p value from t table for

degree of freedom = 10 and t static = 4.032

alpha = 0.005

hence p value = 0.0011

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