In pennsylvania, the average iq score is 101.5. the variable is normally distributed and the population standard deviation is 15. a school superintendent claims that the students in her school district have an iq higher than the average of 101.5. she selects a random sample of 30 students and finds the mean of the test scores is 106.4.

test the claim at α = 0.05

1. state the hypotheses and identify the claim. h0: μ=101.5h1: μ> 101.5this is the claim, and this indicates a right-tailed test
2. find the critical value. for a right-tailed test with α = 0.05, the z-value is +1.65.
3. compute the test statistic.

Let denotes the population mean.

1. Claim : The students in her school district have an IQ higher than the average of 101.5.

As per given , we have

Null hypothesis :

Alternative hypothesis:

∵Alternative hypothesis is right-tailed , this indicates a right-tailed test

Also, Population standard deviation = , we use z-test.

sample size = 30

sample mean =

2. According to the z-table , the critical z-value for the right-tailed test with α = 0.05 is +1.65.

i.e. Critical value = 1.65

3. Test statistic :

Since the calculated z > Critical  z value , so we reject the null hypothesis.

We conclude that we have sufficient evidence at α = 0.05  to support the school superintendent claim that the students in her school district have an IQ higher than the average of 101.5.

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~

its the second choice.

step-by-step explanation:

the elements in the range will be 7 less than the elements in the domain.