Question

(1 point) Julia thinks that she has a special relationship with the number 5. In particular, Julia thinks that she would roll a 5 with a fair 6-sided die more often than you'd expect by chance alone. Suppose p p is the true proportion of the time Julia will roll a 5. (a) State the null and alternative hypotheses for testing Julia's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "<", ">", "=", "not =" and express any values as a fraction e.g. p = 1/3) H0 H 0 = Ha H a = (b) Now suppose Julia makes n = 46 rolls, and a 5 comes up 10 times out of the 46 rolls. Determine the P-value of the test: P-value = (c) Answer the question: Does this sample provide evidence at the 5 percent level that Julia rolls a 5 more often than you'd expect? (Type: Yes or No)

          (1 point) Julia thinks that she has a special relationship with
the number 5. In particular, Julia thinks that she would roll a 5
with a fair 6-sided die more often than you'd expect by chance
alone. Suppose p p is the true proportion of the time Julia will
roll a 5. (a) State the null and alternative hypotheses for testing
Julia's claim. (Type the symbol "p" for the population proportion,
whichever symbols you need of "<", ">", "=", "not =" and
express any values as a fraction e.g. p = 1/3) H0 H 0 = Ha H a =
(b) Now suppose Julia makes n = 46 rolls, and a 5 comes up 10 times
out of the 46 rolls. Determine the P-value of the test: P-value =
(c) Answer the question: Does this sample provide evidence at the 5
percent level that Julia rolls a 5 more often than you'd expect?
(Type: Yes or No)

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Added by Ashley G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jen H

06/19/2023

Step 1

Since a fair 6-sided die has 6 faces, the probability of rolling a 5 by chance alone is 1/6. So, the null and alternative hypotheses are: $H_0: p = \frac{1}{6}$ $H_a: p > \frac{1}{6}$ (b) Show more…

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(1 point) Julia thinks that she has a special relationship with the number 5. In particular, Julia thinks that she would roll a 5 with a fair 6-sided die more often than you'd expect by chance alone. Suppose p p is the true proportion of the time Julia will roll a 5. (a) State the null and alternative hypotheses for testing Julia's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "<", ">", "=", "not =" and express any values as a fraction e.g. p = 1/3) H0 H 0 = Ha H a = (b) Now suppose Julia makes n = 46 rolls, and a 5 comes up 10 times out of the 46 rolls. Determine the P-value of the test: P-value = (c) Answer the question: Does this sample provide evidence at the 5 percent level that Julia rolls a 5 more often than you'd expect? (Type: Yes or No)

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Transcript

00:01 Okay, so here we have julia thinks that she has a special relationship with the number four.

00:04 So when she rolls a four -sided dice, she thinks that she gets a four more often than she's supposed to by chance.

00:09 There are six numbers on the dice, so our null hypothesis is going to be that the probability, or proportion of rolls is going to be one -sixth.

00:24 That she's going to roll it a sixth of the time.

00:27 And then our alternative hypothesis is going to be that p is greater than one -sixth.

00:34 So that's part a.

00:38 Then part b, we're going to actually do the hypothesis test.

00:43 So it says we're going to assume that she makes 42 rolls and she comes up with a four nine times.

00:59 So we're going to take nine divided by 42.

01:04 So we got that p is 0 .21.

01:09 I'll just round it to there, 0 .21.

01:11 So now we want to conduct our hypothesis test and see if this is going to be the case or not.

01:19 So the first thing that i want to do is just choose a confidence level and we'll just do 95 % because that's the most common.

01:30 And so i'll do the z -score negative 1 .96 and 1 .96.

01:36 These are just known values at a 95 % confidence level and it's also on your z -chart if you want to look it up.

01:44 Because we have a sample of at least 30, we can do a z -score.

01:50 So what i'm going to do is convert this into a z -score and this is going to be my p hat, my sample p.

01:55 So it's going to be 0 .21 minus 1 over 6 is 1 .17.

02:05 So i'm just going to write that here.

02:08 They wanted you to write it as a fraction but now when we're plugging it in we're going to have to put it as a decimal.

02:12 0 .17 over square root, it's going to be p...

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