Dr. Cawood\'s class is presented with a large bin that contains small plastic be

Question

Dr. Cawood's class is presented with a large bin that contains small plastic beads. The beads in the box are either purple or white. Dr. Cawood states that 25% of the beads are purple but Oliver, a student in Dr. Cawood's class believes that more than a quarter of the beads in the model box are purple.

a) Select both a null and alternative hypothesis that represent this situation. Be careful of notation.

Select one or more:

HA: p=0.25

HA: p0.25

H0: p<0.25

H0: p>0.25

HA: p0.25

H0: p=0.25

HA: p<0.25

HA: p>0.25

b) Oliver takes a random sample of beads and finds that 17 out of the 43 beads sampled are purple. What is the p-value associated with the hypothesis test in part a?

c) Based on the p-value that you calculated in part b, what conclusion can be made about your hypothesis?

Select one:

There is enough evidence to suggest that the proportion of purple beads in the model box is more than 25%

There is enough evidence to suggest that the proportion of purple beads in the model box is less than 25%

There is enough evidence to suggest that the proportion of purple beads in the model box is equal to 25%

There is not enough evidence to suggest that the proportion of purple beads in the model box is more than 25%

There is not enough evidence to suggest that the proportion of purple beads in the model box is less than 25%

There is not enough evidence to suggest that the proportion of purple beads in the model box is equal to 25%

Explanation / Answer

Ho: p = 0.25
Ha: p > 0.25
----

p-hat = 17/43 = 0.395
----
Test stat: z(0.395) = = (0.395 - 0.25)/sqrt(0.25*0.75/17) = 1.381
---
p-value = P(z > 1.381) = 0.0968

If alpha = 0.05

There is not enough evidence to suggest that the proportion of purple beads in the model box is equal to 25%

p > alpha and null is accepted. THus,

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