1. Spinning a coin, unlike tossing it, may not give heads and tails equal probabilities. I spun a penny 150 times and got 64 heads. We wish to find how significant is this evidence against equal probabilities.

What is the sample proportion of heads?

__________ Round to 3 places.

Heads do not make up half of the sample. Is this sample evidence that the probabilities of heads and tails are different? Let's investigate with a hypothesis test. Takepto be the probability of getting heads in a spin of a penny. Which hypotheses do we want to test?

• H₀:p= 0.5 H_A:p 0.5
• H₀:p= 0.5 H_A:p> 0.5
• H₀:p= 0.5 H_A:p< 0.5
• H₀:p 0.5 H_A:p= 0.5

1. Is the sample independent? Check withn0.05N

__________ 0.05N

Meaning that the population size has to be greater than what?Round to the nearest whole number.

N ____________

Note: The population is all the time that you can spin the penny.

Is the sample large enough for the sampling distribution ofpp^to be approximately normal?Do not round your answers.

np0=___________

n(1p0)=_____________

What is the conclusion about the shape of the sampling distribution ofp^?

• Approximately Normal becausenp010andn(1-p0) 10.
• Unknown shape because not enough information is given in the problem.
• Approximately Normal becausenp0<10andn(p0) <10.
• Approximately Normal because the sample sizen30.
• Approximately Normal regardless of sample size.
• Not approximately Normal becausenp0<10andn(1-p0)<10.

Calculate the following parts assuming the condition are met.

c). Compute theztest statistic.

z= ____________ Round to 2 places.

d). Compute thep-value.____________________________Round to 4 places

e). Based on thep-valuewhat is your conclusion if=0.01?

• Fail to rejectH0. There is sufficient evidence to conclude that when you spin a penny you do not get equal probabilities.
• RejectH0. There is sufficient evidence to conclude that when you spin a penny you do not get equal probabilities.
• Fail to rejectH0. There is insufficient evidence to conclude that when you spin a penny you do not get equal probabilities.
• RejectH0. There is insufficient evidence to conclude that when you spin a penny you do not get equal probabilities.

• 2). You are conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly more than 0.39. You use a significance level of=0.10. H0:p=0.39 HA:p>0.39 You obtain a sample of sizen=482in which there are 222 successes. What is the test statistic for this sample? (Report answer accurate to three decimal places.)

test statistic =__________

What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =__________

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the proportion of women over 40 who regularly have mammograms is more than 0.39.
• There is not sufficient evidence to warrant rejection of the claim that the proportion of women over 40 who regularly have mammograms is more than 0.39.
• The sample data support the claim that the proportion of women over 40 who regularly have mammograms is more than 0.39.
• There is not sufficient sample evidence to support the claim that the proportion of women over 40 who regularly have mammograms is more than 0.39.

3, Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day. A sample of 63 stocks traded on the NYSE that day showed that 23 went up. You are conducting a study to see if the proportion of stocks that went up is significantly more than 0.3. You use a significance level of=0.10. What is the test statistic for this sample? (Report answer accurate to 2 decimal places.)

test statistic =___________

What is the p-value for this sample? (Report answer accurate to 4 decimal places.)

p-value =_____________

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is more than 0.3.
• There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is more than 0.3.
• The sample data support the claim that the proportion of stocks that went up is more than 0.3.
• There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is more than 0.3.
• A well-known brokerage firm executive claimed that 60% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 500 people, 285 of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is smaller than 60% at the 0.05 significance level. The null and alternative hypothesis would be:

H0:=0.6H0:=0.6 HA:>0.6HA:>0.6

H0:p=0.6H0:p=0.6 HA:p>0.6HA:p>0.6

H0:p=0.6H0:p=0.6 HA:p<0.6HA:p<0.6

H0:=0.6H0:=0.6 HA:0.6HA:0.6

H0:=0.6H0:=0.6 HA:<0.6HA:<0.6

H0:p=0.6H0:p=0.6 HA:p0.6HA:p0.6

The test statistic is:_______ (to 2 decimals)

The p-value is ____________ (to 4 decimals)

4."Trydint" bubble-gum company claims that 7 out of 10 people prefer their gum to "Eklypse". Test their claim at the 95-confidence level. The null and alternative hypotheses in symbols would be:

• H0:=0.7H0:=0.7 HA:0.7HA:0.7
• H0:=0.7H0:=0.7 HA:>0.7HA:>0.7
• H0:=0.7H0:=0.7 HA:<0.7HA:<0.7
• H0:p=0.7H0:p=0.7 HA:p0.7HA:p0.7
• H0:p=0.7H0:p=0.7 HA:p>0.7HA:p>0.7
• H0:p=0.7H0:p=0.7 HA:p<0.7HA:p<0.7 The null hypothesis in words would be:
• The proportion of all people that prefer Trydint gum is less than 0.7.
• The proportion of people in a sample that prefers Trydint gum is 0.7.
• The proportion of all people that prefer Trydint gum is greater than 0.7.
• The average of people that prefer Trydint gum is 0.7.
• The average of people that prefer Trydint gum is not 0.7.
• The proportion of people in a sample that prefer Trydint gum is not 0.7
• The proportion of all people that prefer Trydint gum is 0.7

Based on a sample of 270 people, 181 said they prefer "Trydint" gum to "Eklypse". The point estimate is__________ (to 3 decimals)

The 95 % confidence interval is ___________ to ____________ (to 3 decimals)