Question

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:

  

(please enter a decimal)

H1:

  

(Please enter a decimal)

3. The test statistic
4. The p-value = (Please show your answer to 3 decimal places.
5. The p-value is α
6. Based on this, we should the null hypothesis.
7. 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.)

b The p-value for the sample = (Please show your answer to four 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

Answer 1

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