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In: Statistics and Probability

To test Upper H 0 : mu equals20 versus Upper H 1 : mu less than20,...

To test Upper H 0 : mu equals20 versus Upper H 1 : mu less than20, a simple random sample of size nequals 19 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d).

(a) If x overbar = 18 and s= 4.2 , compute the test statistic. (Round to two decimal places as needed.)

(b) Draw a t-distribution with the area that represents the P-value shaded. Which of the following graphs shows the correct shaded region?

(c) Approximate the P-value.

(d) If the researcher decides to test this hypothesis at the a= 0.05 level of significance, will the researcher reject the null hypothesis?

Expert Solution

Solution:
The provided sample mean is x̄ = 18 and the known population standard deviation is

s = 4.2, and the sample size is n = 19.

Null and Alternative Hypotheses:
The following null and alternative hypotheses need to be tested:

Ho: μ = 20
Ha: μ < 20
This corresponds to a one tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

a) Test statistic:

t= -2.08

b) Area of p-value :

c)
Using the P-value approach: The p-value is p = 0.0263, ..using excel formula, =TDIST(2.08,18,1)

and since p = 0.0263< 0.05, it is concluded that the null hypothesis is rejected

d)Conclusion: It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is less than 20, at the 0.05 significance level.

orchestra answered 2 years ago

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