Give a simple student reply to how well they explained the following: Step 1: Check assumptions

Both samples are independent and of size 100

Proportions are not too close to 0 or 1

All values of np and n(1p)are 5 Assumptions are met to use a z-test.

Step 2: State values

We calculate the pooled proportion under H0: p1= p2

p= x1+x2/n1+n2 = (0.40 x 100) + (0.35 x 100) / 200 = 40+35/200 = 75/200 = 0.375

Then the standard error under H0:

SE = p(1-p) (1/n1 + 1/n2) = 0.375(1-0.375) (1/100 + 1/100) = 0.375 x 0.625 x 2/100= 0.234375 x 0.02 = 0.0046875 = 0.0685

Now we compute the z-statistic:

z = p1-p2/SE = 0.40-0.35/0.0685 = 0.05/0.0685 = 0.73

Step 3: Find critical values

Since the alternative hypothesis is H1: p1 > p2, this is a right-tailed test.

At = 0.01, the critical z-value is: z0.01 = 2.33

At = 0.10, the critical z-value is:z0.10 = 1.28

Step 4: Make decisions

We compare our test statistic z = 0.73 to the critical values:

At = 0.01: 0.73 < 2.33 Fail to reject H0

At = 0.10: 0.73 < 1.28 Fail to reject H0

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Final conclusion:

The assumptions for the z-test are satisfied.

The calculated z-statistic is approximately 0.73.

The critical values are:

2.33 at = 0.01

1.28 at = 0.10

Decision:

At = 0.01 Do not reject H0

At = 0.10 Do not reject H0

There is not enough evidence to support that p1>p2 at either significance level.