Math  /  Data & Statistics

Questionwant you to use a calculator program to find a p-value when you already have the Test Statistic. If you have not already accessed it, you need to open the Technology Guide to find P-values (with Examples) Handout found in Content for detailed steps and examples. There is also a video that works through examples of these. You will use the Normalcdf program for this example because the test statistic you will be given is a zz test statistic. You get to the program using 2ND VARS. Follow the directions for a left tailed test for this problem provided on the handout. The bounds you need to enter in your calculator for a left tailed test are specified on the handout. Do not guess. Read and follow the directions. Use Technology to find the p -value for the claim H1: p<0.75\mathrm{p}<0.75, if the test statistic is known to be z=1.74z=-1.74. Will the test statistic, z=1.74z=-1.74, be the upper or lower bound for a left tail test? A. Upper bound, since we want the area to the left of this value for a left tail. B. Lower bound, since we want the area to the right of this value for a left tail.
What is the pp-value? \square Round your answer to 4 decimal places.
Ask my instructor Clear all Check answer 6:11 PM 11/24/2024

Studdy Solution

STEP 1

What is this asking? Given a test statistic of z=1.74z = -1.74 for a left-tailed test, we need to find the p-value using a calculator's `Normalcdf` function, rounding to four decimal places. Watch out! Make sure to use the correct bounds for a left-tailed test in the `Normalcdf` function and don't mix up left and right tails!

STEP 2

1. Identify the distribution and the test type.
2. Determine the appropriate bounds.
3. Calculate the p-value.

STEP 3

We're dealing with a **z test statistic**, which means we're working with the **standard normal distribution**.
This distribution is beautifully symmetrical and centered at zero!
It's the superstar of statistics!

STEP 4

It's a **left-tailed test**, so we're looking for the probability of getting a z-score *less than* or *equal to* our test statistic.
Imagine shading the area under the curve to the *left* of our test statistic.

STEP 5

For a left-tailed test, our **test statistic** (z=1.74z = -1.74) acts as the **upper bound**.
Think of it as the rightmost edge of the shaded region under the curve.

STEP 6

Since the standard normal distribution extends infinitely to the left, we use a very large negative number as our **lower bound**.
Something like 1099-10^{99} (negative ten to the ninety-ninth power) works great!
This essentially captures *all* the area under the curve to the left of our test statistic.

STEP 7

Now, let's use the `Normalcdf` function on our calculator!
We plug in our **lower bound** (1099-10^{99}) and **upper bound** (1.74-1.74).

STEP 8

p-value=Normalcdf(lower=1099,upper=1.74) \text{p-value} = \text{Normalcdf}(\text{lower} = -10^{99}, \text{upper} = -1.74)

STEP 9

Crank those numbers through the calculator, and we get a p-value of approximately **0.04093**.

STEP 10

Finally, let's round that to four decimal places, giving us a **final p-value** of **0.0409**.

STEP 11

The p-value is 0.0409.
The test statistic, z=1.74z = -1.74, is the upper bound for a left-tailed test because we are looking for the area to the left of this value.
So the answer is A!

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