The belief is that the mean number of hours per week of part-time work of high school seniors in a city is 10.5 hours. Data from a simple random sample of 23 high school seniors indicated that their mean number of part-time work was 11.5 with a standard deviation of 1.4. Test whether these data cast doubt on the current belief. (use α = 0.05) Required:
a. State your null and alternative hypotheses.
b. Sketch the rejection region.
c. Calculate the test statistic. Plot this value in your sketch in part b.
d. Determine the P-value for your test.
e. State your conclusions clearly in complete sentences.

a) See step by step explanation

b) See annex

c) t(s) = 3,4255

d) p- value  = 0,00146   or   0,15 %

e) See step by step explanation

Step-by-step explanation:

As n < 30 we use a t-student distribution

Population mean  μ₀ = 10,5

Sample size   n = 23

Degree of freedom      n - 1   =  22

Sample mean    μ  =  11,5

Sample standard deviation   s = 1,4

Confidence Interval  95 %

a) Null Hypothesis                     H₀             μ  =   μ₀

   Alternative Hypothesis         Hₐ              μ  >  μ₀

As CI  = 95 %      α = 5%    or   α = 0,05

We are solving a one tail-test  

With  df  =  22   and     α  = 0,05 in t-table we find t(c) = 1,7171

c)  t(s)  =  (   μ  -  μ₀ ) / s / √n

    t(s)  = ( 11,5 - 10,5 ) / 1,4 / √23

    t(s)  =   1 * 4,7958 / 1,4

    t(s)  =  3,4255

We compare t(s)  and t(c)

t(s) > t(c)   and t(s) is in the rejection region

Then we reject the null hypothesis.

d) P-value for    t(s) = 3,4255  is from t-table   equal to:

We find        for  df = 22    α = 0,001    and   α = 0,005

values of t                            

t                  3,505              2, 819           Δt   =  0,686

α                  0,001               0,005           Δα  =  0,004

with these values we interpolate by rule of three

0,686                          ⇒   0,004

(3,505 - 3,4255)       ⇒       x

x = 0,000463

and  P-value  =  0,00146    or  0,15 %

e) The p-value indicates  we are far away to consider the accptance of H₀

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

i think the answer is b.

step-by-step explanation:

not 100% sure though.