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Two types of phone operating system are being tested to determine

if there is a difference in the proportions of system failures (crashes). Fifteen out of a random sample of 150 phones with $O{S}_1$had system failures within the first eight hours of operation. Nine out of another random sample of 150 phones with $O{S}_2$had system failures within the first eight hours of operation. $O{S}_2$is believed to be more stable (have fewer crashes) than $O{S}_1$.

What can you conclude about the two operating systems?

Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota.

State the null and alternative hypotheses.

a.$H_0:$

b. $H_a$:

Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota.

Calculate the test statistic.

According to a television commercial, $80\%$of dentists agree that Ultrafresh toothpaste is the best on the market.

Indicate if the hypothesis test is for :-

a. independent group means, population standard deviations, and/or variances known

b. independent group means, population standard deviations, and/or variances unknown

c. matched or paired samples

d. single mean

e. two proportions

f. single proportion

Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota.

Does it appear that the proportion of Nevadans who are two or more races is higher than the proportion of NorthDakotans? Why or why not?

Use the following information to answer the next five exercises. A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in Table 10.21. The 鈥渂efore鈥� value is matched to an 鈥渁fter鈥� value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level.

State the null and alternative hypotheses.

Use the following information to answer the next five exercises. A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in Table 10.21. The 鈥渂efore鈥� value is matched to an 鈥渁fter鈥� value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level.

What is the p-value?

Use the following information to answer the next five exercises. A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in Table 10.21. The 鈥渂efore鈥� value is matched to an 鈥渁fter鈥� value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level.

What conclusion can you draw about the software patch?

Use the following information to answer next five exercises. A study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal distribution. Test at the $1\%$ significance level.

What is the p-value?

It is believed that the average grade on an English essay in a particular school system for females is higher than for males. A random sample of $31$females had a mean score of $82$with a standard deviation of three, and a random sample of $25$males had a mean score ofrole="math" localid="1650387947130" $76$ with a standard deviation of four.