Question

2. A test will be conducted to see how long a seven-ounce tube of toothpaste lasts. The researcher wants to establish that the mean time is greater than 30.5 days. From a random sample of size 75, and investigator obtains y ̄ = 32.3 and s = 6.2 days.

   (a) (5 points) Formulate the null and alternative hypotheses. (b) (5 points) Determine the test statistic.

   (c) (5 points) Give the form of the rejection region.
   (d) (5 points) What is the conclusion to your test? Take α = .10.

   (e) (5 points) Based on part (d), what error could you have possibly made?

Answer 1

n=75, =30.5, =0.10

= 32.3, s= 6.2

a)

the null and alternative hypotheses is

Ho: 30.5
Ha: > 30.5

b)

Calculte test statistic

t = 2.514

Test statistic: t = 2.514

c)

calculate t critical values for right tailed test with =0.10 and df= n-1 = 75-1=74

using t table we get

Critical values are = 1.296

decision rule is

Reject Ho if t > 1.296

d)

Reject Ho if t > 1.296

here (t=2.514) > 1.296

hence,

Reject the Null hypothesis (Ho).

Conclusion:
There is sufficient evidence to support the claim that the mean time is greater than 30.5 days.

e)

based on part (d) we possibly made Type I error.

because, type I error occurs when we rejects the true null hypothesis.

here we also have rejected null hypothesis.

hence, there is only chance of type I error to occur.