Photon is a training device that is designed to improve a user's reaction time. Similar devices have been criticized for being too easy to master, but the makers of Photon say that their device is built to give most users room to improve. The makers say that even among professional athletes, the proportion, , who can score the top ranking of "light speed" is less than 16%. A random sample of 110 professional athletes is chosen, and 14 score a ranking of "light speed" while using the device. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the  level of significance, to support the claim that the proportion of all professional athletes who can score a ranking of "light speed" is less than 16% .

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Photon is a training device that is designed to improve a user's reaction time. Similar devices have been criticized for being too easy to master, but the makers of Photon say that their device is built to give most users room to improve. The makers say that even among professional athletes, the proportion, , who can score the top ranking of "light speed" is less than 16%. A random sample of 110 professional athletes is chosen, and 14 score a ranking of "light speed" while using the device.
Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the  level of significance, to support the claim that the proportion of all professional athletes who can score a ranking of "light speed" is less than 16% .

earch
Step 1: Select one-tailed or two-tailed.
O One-tailed
OTwo-tailed
Step 2: Enter the test statistic.
(Round to 3 decimal places.)
Step 3: Shade the area represented by
the p-value.
Step 4: Enter the p-value.
(Round to 3 decimal places.)
3
Explanation
2
St
Check
EPIC
04
(d) Based on your answer to part (c), choose what can be concluded, at the 0.10 level of significance, about the claim made
by the makers of the device.
0.3+
O Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough
evidence to support the claim that less than 16% of professional athletes can score the top-ranking of "light speed."
0.1-
O Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not
enough evidence to support the claim that less than 16% of professional athletes can score the top-ranking of "light
speed."
G
O Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence
to support the claim that less than 16% of professional athletes can score the top-ranking of "light speed."
2
X
1
3
NEXT
X
Ś
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Transcribed Image Text:earch Step 1: Select one-tailed or two-tailed. O One-tailed OTwo-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p-value. Step 4: Enter the p-value. (Round to 3 decimal places.) 3 Explanation 2 St Check EPIC 04 (d) Based on your answer to part (c), choose what can be concluded, at the 0.10 level of significance, about the claim made by the makers of the device. 0.3+ O Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that less than 16% of professional athletes can score the top-ranking of "light speed." 0.1- O Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that less than 16% of professional athletes can score the top-ranking of "light speed." G O Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that less than 16% of professional athletes can score the top-ranking of "light speed." 2 X 1 3 NEXT X Ś 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Acces
Photon is a training device that is designed to improve a user's reaction time. Similar devices have been criticized for being too easy to master, but the makers
of Photon say that their device is built to give most users room to improve. The makers say that even among professional athletes, the proportion, p, who can
score the top ranking of "light speed" is less than 16%. A random sample of 110 professional athletes is chosen, and 14 score a ranking of "light speed" while
using the device.
Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to support the claim that the
proportion of all professional athletes who can score a ranking of "light speed" is less than 16%.
(a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test.
Ho:
H₁:
np =
0
n(1-p) =
p
Standard Normal Distribution
<□
Explanation
DE
Check
X
(b) For your hypothesis test, you will use a Z-test. Find the values of np and n (1-p) to confirm that a Z-test can be used. (One standard is that np ≥ 10
and n (1-p) ≥ 10 under the assumption that the null hypothesis is true.) Here is the sample size and p is the population proportion you are testing.
EPIC
S
(c) Perform a Z-test and find the p-value.
Here is some information to help you with your Z-test.
• The value of the test statistic is given by
X
ô
E
P-P
p(1-p)
Đ
n
• The p-value is the area under the curve to the left of the value of the test statistic.
S
>
NZXT
Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility
6
Transcribed Image Text:Photon is a training device that is designed to improve a user's reaction time. Similar devices have been criticized for being too easy to master, but the makers of Photon say that their device is built to give most users room to improve. The makers say that even among professional athletes, the proportion, p, who can score the top ranking of "light speed" is less than 16%. A random sample of 110 professional athletes is chosen, and 14 score a ranking of "light speed" while using the device. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to support the claim that the proportion of all professional athletes who can score a ranking of "light speed" is less than 16%. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: H₁: np = 0 n(1-p) = p Standard Normal Distribution <□ Explanation DE Check X (b) For your hypothesis test, you will use a Z-test. Find the values of np and n (1-p) to confirm that a Z-test can be used. (One standard is that np ≥ 10 and n (1-p) ≥ 10 under the assumption that the null hypothesis is true.) Here is the sample size and p is the population proportion you are testing. EPIC S (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. • The value of the test statistic is given by X ô E P-P p(1-p) Đ n • The p-value is the area under the curve to the left of the value of the test statistic. S > NZXT Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility 6
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