In pennsylvania the average iq score is 101.5 the variable is normally distributed and the population standard deviation is known to be 15. a school superintendent claims that students in her school district have an iq that is significantly greater than the state average. a random sample of 30 students from her district are selected and the sample mean iq score was 106.4 find the p-value for the test and round to 3 decimal places.

a. 0.0736
b. 0.0465
c. 0.0368
d. 0.05
e. 0.963

P-value = 0.0368

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 101.5

Sample mean, = 106.4

Sample size, n = 30

Alpha, α = 0.05

Population standard deviation, σ = 15

First, we design the null and the alternate hypothesis

We use One-tailed(right) z test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,  

We reject the null hypothesis and accept the alternate hypothesis. Thus, students in Pennsylvania have an IQ that is significantly greater than the state average.

P-value can be calculated with the standard normal table.

P-value = 0.0368

P-value is lower than the significance level.

The student council made more snow cones per hour than the parent volunteers.

Explanation:

To find the number of snow cones made per hour:

XXX

Divide the number of snow cones made

XXX

by the number of hours spent making snow cones.

Parent volunteers

XXX

Number of snow cones:  

120

XXX

Number of hours spent making snow cones:  

5

Number of snow cones per hour:  

120

÷

5

=

24

Student council

XXX

Number of snow cones:  

100

XXX

Number of hours spent making snow cones:  

4

Number of snow cones per hour:  

100

÷

4

=

25

Since the student council made  

25

snow cones per hour and the parent volunteers only made  

24

snow cones per hour:

the student council made more snow cones per hour.

Step-by-step explanation: