State the null hypothesis and the alternative hypothesis for each situation.?

[arber47]

State the null hypothesis and the alternative hypothesis for each situation. Would you use a left-tailed test, a right-tailed test, or a two-tailed test? (8 points each) Please tell me how to do this.

A tire manufacturer says that their tires have an average life of 50,000 miles. A consumer’s group thinks that the average is actually lower.



When fed Old Rat Chow, rats gained an average of 51 grams. The manufacturer believes that New Rat Chow will result in an increased weight gain.



If a coin is “fair” it will land on heads approximately 50% of the time. An inspector believes that a certain coin is not fair.


For each situation, how would you interpret the results of a hypothesis test that
a. rejects the null hypothesis?
b. fails to reject the null hypothesis?
Refer the question 1 to answer question 4, question 2 to answer question 5 and question 3 to answer question 6. (Each question is worth 12 points)

A tire manufacturer says that their tires have an average life of 50,000 miles. A consumer’s group thinks that the average is actually lower.
c. rejects the null hypothesis?
d. fails to reject the null hypothesis?


When fed Old Rat Chow, rats gained an average of 51 grams. The manufacturer believes that New Rat Chow will result in an increased weight gain.
e. rejects the null hypothesis?
f. fails to reject the null hypothesis?


If a coin is “fair” it will land on heads approximately 50% of the time. An inspector believes that a certain coin is not fair.
g. rejects the null hypothesis?
h. fails to reject the null hypothesis?

[lifton]

State the null hypothesis and the alternative hypothesis for each situation. Would you use a left-tailed test, a right-tailed test, or a two-tailed test? (8 points each) Please tell me how to do this.

A tire manufacturer says that their tires have an average life of 50,000 miles. A consumer’s group thinks that the average is actually lower.



When fed Old Rat Chow, rats gained an average of 51 grams. The manufacturer believes that New Rat Chow will result in an increased weight gain.



If a coin is “fair” it will land on heads approximately 50% of the time. An inspector believes that a certain coin is not fair.


For each situation, how would you interpret the results of a hypothesis test that
a. rejects the null hypothesis?
b. fails to reject the null hypothesis?
Refer the question 1 to answer question 4, question 2 to answer question 5 and question 3 to answer question 6. (Each question is worth 12 points)

A tire manufacturer says that their tires have an average life of 50,000 miles. A consumer’s group thinks that the average is actually lower.
c. rejects the null hypothesis?
d. fails to reject the null hypothesis?


When fed Old Rat Chow, rats gained an average of 51 grams. The manufacturer believes that New Rat Chow will result in an increased weight gain.
e. rejects the null hypothesis?
f. fails to reject the null hypothesis?


If a coin is “fair” it will land on heads approximately 50% of the time. An inspector believes that a certain coin is not fair.
g. rejects the null hypothesis?
h. fails to reject the null hypothesis?

1)
"A tire manufacturer says that their tires have an average life of 50,000 miles". So it's truth for now, that mean that it is null hypothesis. The consumer’s group doesn't think so, so they want to test it:
Ho: m?50000
Ha: m<50000
left-tailed (because the alternative hypothesis refers to the left side of graph)
2)
Ho: m?51
Ha: m>51
right-tailed (because the alternative hypothesis refers to the right side of graph)
3)
Ho: p=0.5
Ha: p?0.5
two-tailed test (because we are testing one point)
Let's call t=critical z-score
4)
c)Reject Ho if z <t (z=(x-m)/se)
d)Do not reject Ho if z >t
5)
e)Reject Ho if z >t
f)Do not reject Ho if z <t
6)
g)Reject Ho if z >t or z <-t
h)Do not reject Ho if -t<z<t