The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with o = 7. A random sample of 98 matchboxes shows the average number of matches per box to be 41.9. Using a 1% level of significance, can you say that the average number of matches per box is more than 40? What are we testing in this problem? O single proportion O single mean (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H = 40; H: u < 40 O Ho: p = 40; H;: p > 40 Ο Hρ μ= 40; Η: μ > 40 O Ho: p = 40; Hạ: p < 40 O Họ: p = 40; H;: p- 40 O Ho: H = 40; H: u- 40 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal, since we assume that x has a normal distribution with known o. O The Student's t, since we assume that x has a normal distribution with unknown o. O The Student's t, since we assume that x has a normal distribution with known o. O The standard normal, since we assume that x has a normal distribution with unknown o. What is the value of the sample test statistic? (Round your answer to two decimal places.)

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The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with o = 7. A random sample of 98 matchboxes shows the average number of matches per box to be
41.9. Using a 1% level of significance, can you say that the average number of matches per box is more than 40?
What are we testing in this problem?
O single proportion
O single mean
(a) What is the level of significance?
State the null and alternate hypotheses.
O Ho: u = 40; H1: µ < 40
O Ho: p = 40; H1: p > 40
O Ho: u = 40; H1: u > 40
O Ho: p = 40; H1: p < 40
O Họ: p = 40; H1: p + 40
O Họ: u = 40; H: u * 40
(b) What sampling distribution will you use? What assumptions are you making?
O The standard normal, since we assume that x has a normal distribution with known o.
O The Student's t, since we assume that x has a normal distribution with unknown o.
O The Student's t, since we assume that x has a normal distribution with known o.
O The standard normal, since we assume that x has a normal distribution with unknown o.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
Transcribed Image Text:The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with o = 7. A random sample of 98 matchboxes shows the average number of matches per box to be 41.9. Using a 1% level of significance, can you say that the average number of matches per box is more than 40? What are we testing in this problem? O single proportion O single mean (a) What is the level of significance? State the null and alternate hypotheses. O Ho: u = 40; H1: µ < 40 O Ho: p = 40; H1: p > 40 O Ho: u = 40; H1: u > 40 O Ho: p = 40; H1: p < 40 O Họ: p = 40; H1: p + 40 O Họ: u = 40; H: u * 40 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal, since we assume that x has a normal distribution with known o. O The Student's t, since we assume that x has a normal distribution with unknown o. O The Student's t, since we assume that x has a normal distribution with known o. O The standard normal, since we assume that x has a normal distribution with unknown o. What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find (or estimate) the P-value.
O P-value > 0.250
O 0.125 < P-value < 0.250
O 0.050 < P-value < 0.125
O 0.025 < P-value < 0.050
O 0.005 < P-value < 0.025
O P-value < 0.005
Sketch the sampling distribution and show the area corresponding to the P-value.
o-4
-2
-2
AA
P-value
P-value
O -4
-2
o-4
-2
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret vour conclusion in the context of the anolication.
Transcribed Image Text:(c) Find (or estimate) the P-value. O P-value > 0.250 O 0.125 < P-value < 0.250 O 0.050 < P-value < 0.125 O 0.025 < P-value < 0.050 O 0.005 < P-value < 0.025 O P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. o-4 -2 -2 AA P-value P-value O -4 -2 o-4 -2 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret vour conclusion in the context of the anolication.
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