Question

In: Statistics and Probability

Test the null hypothesis H0:μ=3.8against the alternative hypothesis HA:μ≠3.8, based on a random sample of 35...

Test the null hypothesis H0:μ=3.8against the alternative hypothesis HA:μ≠3.8, based on a random sample of 35 observations drawn from a normally distributed population with x¯=4 and σ=0.89.

a) What is the value of the test statistic?

Round your response to at least 3 decimal places.

   

b) What is the appropriate p-value?

Round your response to at least 3 decimal places.

   

c) Is the null hypothesis rejected at:

i) the 5% level of significance?      NoYesClick for List  

ii) the 10% level of significance?      NoYesClick for List  

Solutions

Expert Solution

Solution :

= 3.8

=4

=0.89

n = 35

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 3.8

Ha :     3.8

a ) Test statistic = z

= ( - ) / / n

= (4 -3.8) / 0.89 / 35

= 1.33

Test statistic = z = 1.33

b ) P(z >1.33 ) = 1 - P(z < 1.33 ) = 1 -0.9082

P-value =2 *0.0918 =0.184

c ) = 0.05  

P-value >

0.184 > 0.05

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that

= 0.10

P-value >

0.184 > 0.10

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that


Related Solutions

Test the null hypothesis H0:μ=3.8against the alternative hypothesis HA:μ<3.8, based on a random sample of 25...
Test the null hypothesis H0:μ=3.8against the alternative hypothesis HA:μ<3.8, based on a random sample of 25 observations drawn from a normally distributed population with x¯=3.6 and σ=0.72. a) What is the value of the test statistic? Round your response to at least 3 decimal places.     b) What is the appropriate p-value? Round your response to at least 3 decimal places.     c) Is the null hypothesis rejected at: i) the 10% level of significance?      YesNoClick for List   ii) the...
Test the null hypothesis H0:μ=3.3against the alternative hypothesis HA:μ≠3.3, based on a random sample of 37...
Test the null hypothesis H0:μ=3.3against the alternative hypothesis HA:μ≠3.3, based on a random sample of 37 observations drawn from a normally distributed population with x¯=3.5 and σ=0.89. a) What is the value of the test statistic? Round your response to at least 3 decimal places.     b) What is the appropriate p-value? Round your response to at least 3 decimal places.     c) Is the null hypothesis rejected at: i) the 5% level of significance?      YesNoClick for List   ii) the...
Consider the following hypothesis test. H0: μ ≥ 35 Ha: μ < 35 A sample of...
Consider the following hypothesis test. H0: μ ≥ 35 Ha: μ < 35 A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use α = 0.01. (a) x = 34 and s = 5.2 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) *PLEASE GO INTO DETAIL WHEN EXPLAINING THIS STEP! How do you...
Consider the following hypothesis test. H0: μ ≥ 35 Ha: μ < 35 A sample of...
Consider the following hypothesis test. H0: μ ≥ 35 Ha: μ < 35 A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use α = 0.01. (a) x = 34 and s = 5.3 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Chose one of the following. Reject...
For a two-tailed hypothesis test at the significance level alpha, the null hypothesis H0: μ =...
For a two-tailed hypothesis test at the significance level alpha, the null hypothesis H0: μ = μ0 will be rejected in favor of the alternative hypothesis Ha: μ≠ μ0 if and only if μ0 lies outside the (1 - α) level confidence interval for μ. Illustrate the preceding relationship by obtaining the appropriate one-mean z-interval for the data below. Suppose the mean height of women age 20 years or older in a certain country is 62.8 inches. One hundred randomly...
A test of the null hypothesis H0: μ = μ0 gives test statistic z = −0.45....
A test of the null hypothesis H0: μ = μ0 gives test statistic z = −0.45. (Round your answers to four decimal places.) (a) What is the P-value if the alternative is Ha: μ > μ0? (b) What is the P-value if the alternative is Ha: μ < μ0? (c) What is the P-value if the alternative is Ha: μ ≠ μ0?
Given the following hypothesis: H0: μ = 100 H1: μ ≠ 100 A random sample of...
Given the following hypothesis: H0: μ = 100 H1: μ ≠ 100 A random sample of six resulted in the following values: 118 ,120 ,107 ,115 ,115 ,107 Using the 0.02 significance level, can we conclude that the mean is different from 100? a. What is the decision rule? (Negative answer should be indicated by a minus sign. Round the final answers to 3 decimal places.) Reject H0: μ = 100 and accept H1: μ ≠ 100 when the test...
Given the following hypothesis: H0: μ = 100 H1: μ ≠ 100 A random sample of...
Given the following hypothesis: H0: μ = 100 H1: μ ≠ 100 A random sample of six resulted in the following values: 114 120 119 108 113 108 Using the 0.01 significance level, can we conclude that the mean is different from 100? a. What is the decision rule? (Negative answer should be indicated by a minus sign. Round the final answers to 3 decimal places.) Reject H0: μ = 100 and accept H1: μ ≠ 100 when the test...
Consider the following hypothesis test. H0: μ ≤ 50 Ha: μ > 50 A sample of...
Consider the following hypothesis test. H0: μ ≤ 50 Ha: μ > 50 A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use α = 0.05. (Round your answers to two decimal places.) (a) x = 52.3 Find the value of the test statistic. = State the critical values for the rejection rule. (If the test is one-tailed, enter NONE...
Consider the following hypothesis test. H0: μ ≤ 25 Ha: μ > 25 A sample of...
Consider the following hypothesis test. H0: μ ≤ 25 Ha: μ > 25 A sample of 40 provided a sample mean of 26.1. The population standard deviation is 6. (a) Find the value of the test statistic. (Round your answer to two decimal places.) (b) Find the p-value. (Round your answer to four decimal places.) p-value = (c) At α = 0.01,state your conclusion. (d) State the critical values for the rejection rule. (Round your answer to two decimal places....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT