Question

# 1. Only about 15% of all people can wiggle their ears. Is this percent higher for...

1.

Only about 15% of all people can wiggle their ears. Is this percent higher for millionaires? Of the 303 millionaires surveyed, 48 could wiggle their ears. What can be concluded at the α

= 0.10 level of significance?

1. For this study, we should use
1. The null and alternative hypotheses would be:

H0:

H1:

1. The test statistic
3. The p-value is α
4. Based on this, we should the null hypothesis.
5. Thus, the final conclusion is that

a The data suggest the population proportion is not significantly higher than 15% at α = 0.10, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is equal to 15%.

b The data suggest the populaton proportion is significantly higher than 15% at α = 0.10, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is higher than 15%.

c The data suggest the population proportion is not significantly higher than 15% at α = 0.10, so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is higher than 15%.

2.

You wish to test the following at a significance level of α=0.05.

H0:p=0.85
H1:p>0.85

You obtain a sample of size n=250 in which there are 225 successful observations.

For this test, we use the normal distribution as an approximation for the binomial distribution.

For this sample...

a The test statistic (z) for the data = (Please show your answer to three decimal places.)

c The p-value is... greater than α or less than (or equal to) α

d Base on this, we should...

• fail to reject the null hypothesis
• accept the null hypothesis
• reject the null hypothesis

As such, the final conclusion is that...

• The sample data suggest that the population proportion is significantly greater than 0.85 at the significant level of α = 0.05
• The sample data suggest that the population proportion is not significantly greater than 0.85 at the significant level of α = 0.05

My dear student I am allow to solve the one question at a time. So I solved the first question in the picture.

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