Arandom sample of 25 values is drawn from a mound-shaped and symmetrical distribution. the sample mean is 10 and the sample standard deviation is 2. use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 9.5.
(a) is it appropriate to use a student's t distribution? explain. how many degrees of freedom do we use?
(b) what are the hypotheses?
(c) compute the sample test statistic t.
(d) estimate the p-value for the test.
(e) do we reject or fail to reject h_0?
(f) interpret the results.

Step-by-step explanation:

Given that random sample of 25 values is drawn from a mound-shaped and symmetrical distribution. The sample mean is 10 and the sample standard deviation is 2.

95 % CI for mean  9.1744 to 10.8256

Since p >0.05 accept null hypothesis.

a) Yes because std dev sigma not known.  df = 24

b)

H0:  x bar = 9.5

Ha: x bar not equals 9.5

c) t-statistic  1.250

d) P = 0.2234

e) We fail to reject null hypothesis

f) There is no statistical evidence at 5% level to fail to reject H0.

Yes, it is directly proportional.

Step-by-step explanation:

Since Anna does a sit-up at a certain amount of time, then we have two quantities we are comparing: a sit up and the amount of time it takes.

It is said that the tired she gets, the more time she uses. Therefore, as her tiredness increases, the amount of time also increases. This implies that the quantities are proportional, directly proportional.