# (Answered) MATH399N Week 7 – Developing Hypothesis and Understanding Possible Conclusions for Mean

Question

Determine the Type I error if the null hypothesis, H0, is: the percentage of homes in the city that are not up to the current electric codes is no more than 10%.

And, the alternative hypothesis, Ha, is: the percentage of homes in the city that are not up to the current electric codes is more than 10%.

# Question

Suppose the null hypothesis, H0, is at least 70% of customers, who shop at a particular sporting good store, do not shop at any other sporting goods stores.

And the alternative hypothesis, Ha, is less than 70% of customers, who shop at a particular sporting good store, do not shop at any other sporting goods stores.

What is the Type I error in this scenario?

# Question

Suppose the null hypothesis, H0, is a surgical procedure is successful at least 80% of the time.
And the alternative hypothesis, Ha, states the doctors’ claim, which is a surgical procedure is successful less than 80% of the time.

Which of the following gives β, the probability of a Type II error?

# Question

A consumer protection company is testing a seat belt to see how much force it can hold. The null hypothesis, H0, is that the seat belt can hold at least 5000 pounds of force. The alternative hypothesis, Ha, is that the seat belt can hold less than 5000 pounds of force.

What is a Type II error in this scenario?

Question

Determine the Type II error if the null hypothesis, H0, is: a wooden ladder can withstand weights of 250 pounds and less.

Question

Is the test below left-, right-, or two-tailed?

H0:p=0.39, Ha:p≠0.39

# Question

Which graph below corresponds to the following hypothesis test?

H0:p=8.1, Ha:p>8.1

# Question

Which of the following results in a null hypothesis p=0.44 and alternative hypothesis p<0.44?

# Question

Which of the following results in a null hypothesis p=0.69 and alternative hypothesis p>0.69?

# Question

Which of the following results in a null hypothesis p=0.61 and alternative hypothesis p>0.61?

Question

Gail, a baker, claims that her bread height is not equal to 14 cm, on average. Several of her customers do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She bakes 15 loaves of bread. The mean height of the sample loaves is 13.8 cm. Gail knows from experience that the standard deviation for her bread height is 0.7 cm.

• H0: μ=14; Ha: μ≠14
• α=0.05(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Question

Suppose a pitcher claims that his pitch speed is less than 43 miles per hour, on average. Several of his teammates do not believe him, so the pitcher decides to do a hypothesis test, at a 10% significance level, to persuade them. He throws 19 pitches. The mean speed of the sample pitches is 35 miles per hour. The pitcher knows from experience that the standard deviation for his pitch speed is 6 miles per hour.

• H0: μ=43; Ha: μ<43
• α=0.1(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Question

Floretta, a pitcher, claims that her pitch speed is less than 46 miles per hour, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She throws 24 pitches. The mean speed of the sample pitches is 37 miles per hour. Floretta knows from experience that the standard deviation for her pitch speed is 5 miles per hour.

• H0: μ=46; Ha: μ<46
• α=0.05(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Question

Lexie, a bowler, claims that her bowling score is more than 140 points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She bowls 18 games. The mean score of the sample games is 155 points. Lexie knows from experience that the standard deviation for her bowling score is 17 points.

• H0: μ=140; Ha: μ>140
• α=0.05(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Question

Which of the hypothesis tests listed below is a left-tailed test? Select all correct answers.

Question

Which graph below corresponds to the following hypothesis test?

H0:X=14.7, Ha:X≠14.7

Question

Suppose the null hypothesis, H0, is: the mean age of the horses on a ranch is 6 years. What is the Type II error in this scenario?

# Question

A study claims that the mean age of online dating service users is 40 years. Some researchers think this is not accurate and want to show that the mean age is not 40 years.

Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.

# Question

Which of the following results in a null hypothesis μ=31 and alternative hypothesis μ<31?

Question

Suppose the null hypothesis, H0, is: the mean age of the horses on a ranch is 6 years. What is the Type I error in this scenario?

You cannot conclude that the mean age of the horses is not 6 years when, in fact, it is.

Question

Jolyn, a golfer, claims that her drive distance is not equal to 222 meters, on average. Several of her friends do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She hits 11 drives. The mean distance of the sample drives is 218 meters. Jolyn knows from experience that the standard deviation for her drive distance is 14 meters.

• H0: μ=222; Ha: μ≠222
• α=0.05(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Question

Olivia, a golfer, claims that her drive distance is more than 174 meters, on average. Several of her friends do not believe her, so she decides to do a hypothesis test, at a 10% significance level, to persuade them. She hits 15 drives. The mean distance of the sample drives is 188 meters. Olivia knows from experience that the standard deviation for her drive distance is 14 meters.

• H0: μ=174; Ha: μ>174
• α=0.1(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

# Solution:

Question

Determine the Type I error if the null hypothesis, H0, is: the percentage of homes in the city that are not up to the current electric codes is no more than 10%.

And, the alternative hypothesis, Ha, is: the percentage of homes in the city that are not up to the current electric codes is more than 10%.

There is sufficient evidence to conclude that more than 10% of homes in the city are not up to the current electrical codes when, in fact, there are no more than 10% that are not up to the current electric codes.

# Question

Suppose the null hypothesis, H0, is at least 70% of customers, who shop at a particular sporting good store, do not shop at any other sporting goods stores.

And the alternative hypothesis, Ha, is less than 70% of customers, who shop at a particular sporting good store, do not shop at any other sporting goods stores.

What is the Type I error in this scenario?