The one-sample t statistic for testing H0 : µ = 10 versus Ha : µ > 10 from a sam

Question

The one-sample t statistic for testing H0 : µ = 10 versus Ha : µ > 10 from a sample of n = 18 observations has the value t = 2.05.

i. What are the degrees of freedom for this statistic?

ii. Give the two critical values from the t-distribution table that bracket t and express the two values using the notation t(k) with appropriate and k.

iii. Between what two values does the P-value of the test fall?

iv. Is the value t = 2.05 significant at the 5% level? Is it significant at the 1% level? v. Using R, find the exact P-value of t = 2.05.

Explanation / Answer

Given that the one-sample t statistic for testing H0 : µ = 10 versus Ha : µ > 10 from a sample of n = 18 observations has the value t = 2.05.

i. What are the degrees of freedom for this statistic?

degrees of freedom = n-1 = 18-1 = 17

ii. Give the two critical values from the t-distribution table that bracket t and express the two values using the notation t(k) with appropriate and k

This probability we can find by using EXCEL.

=TINV(alpha/2, deg_freedom)

where alpha = level of significance = 5% = 0.05

critical value = 2.4581

at 1%,

critical value = 3.2224

at 5% P-value in EXCEL is,

=TDIST(x, deg_freedom)

where x is test statistic value.

deg_freedom = 17

P-value = 0.0281

at 1% also P-value = 0.0281

We reject H0 at 5% level of significance.

Conclusion : Population mean is greator than 10.

At 1% level of significance accept H0.

Conclusion : Population mean is 10.

The test statistic 2.10 lies between 1.740 and 2.110.

And corresponding value is lies between 0.05 to 0.025.

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