Question 1

In performing hypothesis tests about the population mean,the population standard deviation should be used if it is known.If it is not known,which of the following statistical test should be used? A)z test of a population mean B)t test of a population mean C)z test of a population proportion D)$\chi$² test of a population variance E)t test of a population proportion

Accepted Answer

When the population standard deviation is unknown, the t test of a population mean should be used. This test is appropriate when the sample size is small (less than 30) or when the population variance is not known.

Question 2

In performing hypothesis tests about the population mean,the population standard deviation should be used if it is known.If it is not known,a t test can be used to test the mean if ___.
A)the sample size is at least thirty
B)the sample is random
C)the population mean is known
D)the population is normally distributed
E)the population is chi-square distributed

Accepted Answer

The answer of In performing hypothesis tests about the population...

Question 3

In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9,a random sample of 16 items is selected.The sample mean is 7.1 and the sample standard deviation is 2.4.It can be assumed that the population is normally distributed.The observed "t" value for this problem is ___.
A)0.05
B)0.20
C)0.33
D)1.33
E)1.43

Accepted Answer

The answer of In performing a hypothesis test where the...

Question 4

Consider the following null and alternative hypotheses: H_o: p $\le$ 0.16 H_a: p > 0.16 These hypotheses ___. A)indicate a one-tailed test with a rejection area in the right tail B)indicate a one-tailed test with a rejection area in the left tail C)indicate a two-tailed test D)are established incorrectly E)are not mutually exclusive

Accepted Answer

The alternative hypothesis suggests that the true proportion is greater than 0.16, so the rejection area is in the right tail. Therefore, it is a one-tailed test with the rejection area in the right tail.

Question 5

Consider the following null and alternative hypotheses: H_o: p $\ge$ 0.16 H_a: p < 0.16 These hypotheses ___. A)indicate a one-tailed test with a rejection area in the right tail B)indicate a one-tailed test with a rejection area in the left tail C)indicate a two-tailed test D)are established incorrectly E)are not mutually exclusive

Accepted Answer

The null hypothesis (p ≤ 0.16) is being tested against an alternative hypothesis (p > 0.16), indicating a one-tailed test with a rejection area in the right tail.

Question 6

The diameter of 3.5 centimetre discs is normally distributed.Periodically,quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs.If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment;otherwise,the punching process continues.The last sample showed a mean and standard deviation of 3.49 and 0.08 centimetres,respectively.Using $\alpha$ = 0.05,the appropriate decision is ___.
A)reject the null hypothesis and shut down the punch
B)reject the null hypothesis and do not shut down the punch
C)do not reject the null hypothesis and shut down the punch
D)do not reject the null hypothesis and do not shut down the punch
E)do nothing

Accepted Answer

The null hypothesis is that the mean diameter is equal to 3.5 cm. The alternative hypothesis is that the mean diameter is not equal to 3.5 cm. 
Using the sample data, we can calculate the test statistic:

t = (3.49 - 3.5) / (0.08 / sqrt(16)) = -1.0

Using a two-tailed t-test with 15 degrees of freedom and a significance level of 0.05 (or F1F1F1S1F1F1F10 = 0.05), we find that the critical value is ±2.131. Since the test statistic (-1.0) is not in the rejection region, we fail to reject the null hypothesis. Therefore, we do not shut down the punch. The correct answer is D - do not reject the null hypothesis and do not shut down the punch.

Question 7

In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9,a random sample of 16 items is selected.The sample mean is 7.1 and the sample standard deviation is 2.4.It can be assumed that the population is normally distributed.The level of significance is selected as 0.05.The decision rule for this problem is to reject the null hypothesis if the observed "t" value is ___.
A)less than -2.131 or greater than 2.131
B)less than -1.761 or greater than 1.761
C)less than -1.753 or greater than 1.753
D)less than -2.120 or greater than 2.120
E)less than -3.120 or greater than 3.120

Accepted Answer

The answer of In performing a hypothesis test where the...

Question 8

A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the riding.She has her assistants randomly sample 200 eligible voters in the riding by telephone and only 90 declare that they support her candidate.The observed z value for this problem is ___.
A)-4.33
B)4.33
C)0.45
D)-.31
E)2.33

Accepted Answer

To find the observed z-value, we must first find the sample proportion:

p̂ = 90/200 = 0.45

Then we can calculate the z-value using the formula:

z = (p̂ - p) / sqrt(p*(1-p)/n)

where p is the hypothesized proportion (60%) and n is the sample size (200).

z = (0.45 - 0.6) / sqrt(0.6*(1-0.6)/200)

z = -4.33

Therefore, the observed z-value is -4.33, which corresponds to choice (A).

Question 9

A company believes that it controls more than 30% of the total market share for one of its products.To prove this belief,a random sample of 144 purchases of this product is contacted.It is found that 50 of the 144 purchased this company's brand of the product.If a researcher wants to conduct a statistical test for this problem,the alternative hypothesis would be ___.
A)the population proportion is less than 0.30
B)the population proportion is greater than 0.30
C)the population proportion is not equal to 0.30
D)the population mean is less than 40
E)the population mean is greater than 40

Accepted Answer

The alternative hypothesis should always state what we are trying to prove, which in this case is that the company controls more than 30% of the market share. Therefore, the alternative hypothesis should be that the population proportion is greater than 0.30.

Question 10

Ophelia O'Brien,VP of Consumer Credit of Credit First Banks (CFB),monitors the default rate on personal loans at the CFB member banks.One of her standards is "no more than 5% of personal loans should be in default." On each Friday,the default rate is calculated for a sample of 500 personal loans.Last Friday's sample contained 30 defaulted loans.Ophelia's null hypothesis is ___.
A)p > 0.05
B)p = 0.05
C)n = 30
D)n = 500
E)n = 0.05

Accepted Answer

The answer of Ophelia O'Brien,VP of Consumer Credit of Credit...

Question 11

In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9,a random sample of 16 items is selected.The sample mean is 7.1 and the sample standard deviation is 2.4.It can be assumed that the population is normally distributed.The level of significance is selected as 0.05.The table "t" value for this problem is ___.
A)1.753
B)2.947
C)2.120
D)2.131
E)2.311

Accepted Answer

Since the sample size is less than 30 and the population standard deviation is unknown, we need to use a t-test. The null hypothesis is that the population mean is 6.9, and the alternative hypothesis is that the population mean is not equal to 6.9 (two-tailed test). The level of significance is 0.05, so the critical t-value for a two-tailed test with 15 degrees of freedom is 2.131. Therefore, the answer is D.

Question 12

Consider the following null and alternative hypotheses: H_o: p = 0.16 H_a: p $\neq$ 0.16 These hypotheses ___. A)indicate a one-tailed test with a rejection area in the right tail B)indicate a one-tailed test with a rejection area in the left tail C)indicate a two-tailed test D)are established incorrectly E)are not mutually exclusive

Accepted Answer

The null hypothesis states that the population proportion is equal to 0.16, while the alternative hypothesis states that it is not equal to 0.16, indicating a two-tailed test.

Question 13

Suppose a researcher is testing a null hypothesis that $\mu$ = 61.A random sample of n = 36 is taken resulting in a sample mean of 63 and s = 9.The observed t value is ___.
A)-0.22
B)0.22
C)1.33
D)8.08
E)7.58

Accepted Answer

The observed t value can be calculated using the formula:

t = (x̄ - μ) / (s / √n)

where x̄ is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (63 - 61) / (9 / √36) = 2 / 3 = 0.67

The t value corresponding to a two-tailed test with 35 degrees of freedom and a significance level of 0.05 is 2.032. Since our calculated t value (0.67) is smaller than the critical t value (2.032), we fail to reject the null hypothesis.

Therefore, the observed t value is not significant and the answer is (C) 1.33.

Question 14

A company believes that it controls more than 30% of the total market share for one of its products.To prove this belief,a random sample of 144 purchases of this product is contacted.It is found that 50 of the 144 purchased this company's brand of the product.If a researcher wants to conduct a statistical test for this problem,the observed z value would be ___.
A)0.05
B)0.103
C)0.35
D)1.24
E)1.67

Accepted Answer

To calculate the observed z value, we use the following formula:

z = (p - P) / sqrt(P(1-P)/n)

where p is the proportion of purchases that bought the company's brand out of the sample (in this case 50/144 = 0.347), P is the proportion we want to test (in this case P = 0.30), and n is the sample size (in this case n = 144).

Plugging in the numbers, we get:

z = (0.347 - 0.30) / sqrt(0.3*0.7/144) = 1.24

Therefore, the observed z value is 1.24, which corresponds to choice D.

Question 15

The diameter of 3.5 centimetre discs is normally distributed.Periodically,quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs.If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment;otherwise,the punching process continues.The null hypothesis is ___.
A)n $\neq$ 16
B)n = 16
C)$\mu$= 3.5
D)$\mu$ $\neq$ 3.5
E)$\mu$ ≥ 3.5

Accepted Answer

The answer of The diameter of 3.5 centimetre discs is...

Question 16

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8,a random sample of 25 items is selected.The sample mean is 4.1 and the sample standard deviation is 1.4.It can be assumed that the population is normally distributed.The level of significance is selected to be 0.10.The table "t" value for this problem is ___.
A)1.318
B)1.711
C)2.492
D)2.797
E)3.227

Accepted Answer

The test statistic for the two-tailed hypothesis test can be calculated using the formula:

t = (x̄ - μ) / (s / sqrt(n))

where x̄ is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (4.1 - 4.8) / (1.4 / sqrt(25))
t = -2 / 0.28
t = -7.14 (rounded to two decimal places)

The critical values for a two-tailed hypothesis test at level of significance α = 0.10 and degrees of freedom (df) = n-1 = 24 can be found using a t-distribution table. The table "t" value for df = 24 and α/2 = 0.05 is 1.711.

Since the calculated t-value (-7.14) is outside the rejection region defined by the critical values ±1.711, we reject the null hypothesis and conclude that the population mean is not equal to 4.8.

Therefore, the table "t" value for this problem is 1.711 (B).

Question 17

The diameter of 3.5 centimetre discs is normally distributed.Periodically,quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs.If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment;otherwise,the punching process continues.The last sample showed a mean and standard deviation of 3.49 and 0.08 centimetres,respectively.Using $\alpha$ = 0.05,the critical "t" values are ___.
A)-2.120 and 2.120
B)-2.131 and 2.131
C)-1.753 and 1.753
D)-1.746 and 1.746
E)-2.567 and 2.567

Accepted Answer

Since the sample size is 16, we need to use a t-distribution with 15 degrees of freedom. Using F1F1F1S1F1F1F10 = 0.05, we split the significance level equally between the two tails of the distribution, giving us a 0.025 probability in each tail. From a t-distribution table with 15 degrees of freedom, we find that the critical values are -2.131 and 2.131. Therefore, the answer is B.

Question 18

A company believes that it controls more than 30% of the total market share for one of its products.To prove this belief,a random sample of 144 purchases of this product is contacted.It is found that 50 of the 144 purchased this company's brand of the product.If a researcher wants to conduct a statistical test for this problem,the test would be ___.
A)a one-tailed test
B)a two-tailed test
C)an alpha test
D)a finite population test
E)a finite sample test

Accepted Answer

Since the company believes it controls more than 30% of the market share, the hypothesis being tested would be one-tailed (specifically, an upper-tailed test). The null hypothesis would be that the company controls 30% or less of the market share, while the alternative hypothesis would be that the company controls more than 30% of the market share. Therefore, a one-tailed test would be appropriate for this scenario.

Question 19

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8,a random sample of 25 items is selected.The sample mean is 4.1 and the sample standard deviation is 1.4.It can be assumed that the population is normally distributed.The observed "t" value for this problem is ___.
A)-12.5
B)12.5
C)-2.5
D)-0.7
E)0.7

Accepted Answer

The observed t-value can be calculated using the formula:
t = (sample mean - null hypothesis value) / (sample standard deviation/√sample size)

Substituting the given values, we get:
t = (4.1 - 4.8) / (1.4/√25)
t = -0.7

Therefore, the observed t-value for this problem is -0.7, which corresponds to choice C.

Question 20

The diameter of 3.5 centimetre discs is normally distributed.Periodically,quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs.If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment;otherwise,the punching process continues.The last sample showed a mean and standard deviation of 3.55 and 0.08 centimetres,respectively.Using  $\alpha$ = 0.05,the appropriate decision is ___.
A)reject the null hypothesis and shut down the punch
B)reject the null hypothesis and do not shut down the punch
C)do not reject the null hypothesis and shut down the punch
D)do not reject the null hypothesis and do not shut down the punch
E)do nothing

Accepted Answer

The answer of The diameter of 3.5 centimetre discs is...

Quiz 9: Statistical Inference: Hypothesis Testing for Single Populations

In performing hypothesis tests about the population mean,the population standard deviation should be used if it is known.If it is not known,which of the following statistical test should be used?

In performing hypothesis tests about the population mean,the population standard deviation should be used if it is known.If it is not known,a t test can be used to test the mean if ___.

Consider the following null and alternative hypotheses: Ho: p ≤\le≤ 0.16 Ha: p > 0.16 These hypotheses ___.

Consider the following null and alternative hypotheses: Ho: p ≥\ge≥ 0.16 Ha: p < 0.16 These hypotheses ___.

A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the riding.She has her assistants randomly sample 200 eligible voters in the riding by telephone and only 90 declare that they support her candidate.The observed z value for this problem is ___.

Consider the following null and alternative hypotheses: Ho: p = 0.16 Ha: p ≠\neq= 0.16 These hypotheses ___.

Suppose a researcher is testing a null hypothesis that μ\muμ = 61.A random sample of n = 36 is taken resulting in a sample mean of 63 and s = 9.The observed t value is ___.

Consider the following null and alternative hypotheses: H_o: p $\le$ 0.16 H_a: p > 0.16 These hypotheses ___.

Consider the following null and alternative hypotheses: H_o: p $\ge$ 0.16 H_a: p < 0.16 These hypotheses ___.

Consider the following null and alternative hypotheses: H_o: p = 0.16 H_a: p $\neq$ 0.16 These hypotheses ___.

Suppose a researcher is testing a null hypothesis that $\mu$ = 61.A random sample of n = 36 is taken resulting in a sample mean of 63 and s = 9.The observed t value is ___.