{"id":184390,"date":"2025-01-20T20:06:01","date_gmt":"2025-01-20T20:06:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=184390"},"modified":"2025-01-20T20:06:03","modified_gmt":"2025-01-20T20:06:03","slug":"a-survey-claims-that-9-out-of-10-doctors-recommend-aspirin-for-their-patients-with-headaches","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/20\/a-survey-claims-that-9-out-of-10-doctors-recommend-aspirin-for-their-patients-with-headaches\/","title":{"rendered":"A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches"},"content":{"rendered":"\n

51) A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to<\/p>\n\n\n\n

A) -4.12.<\/p>\n\n\n\n

B) -2.33.<\/p>\n\n\n\n

C) -1.86.<\/p>\n\n\n\n

D) -0.07.<\/p>\n\n\n\n

52) A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected. Suppose that the test statistic is -2.20. Can you conclude that H<\/em>0 should be rejected at the (a) \u03b1 <\/em>= 0.10, (b) \u03b1 <\/em>= 0.05, and (c) \u03b1 <\/em>= 0.01 level of Type I error?<\/p>\n\n\n\n

A) (a) yes; (b) yes; (c) yes<\/p>\n\n\n\n

B) (a) no; (b) no; (c) no<\/p>\n\n\n\n

C) (a) no; (b) no; (c) yes<\/p>\n\n\n\n

D) (a) yes; (b) yes; (c) no<\/p>\n\n\n\n

53) A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected. Suppose you reject the null hypothesis. What conclusion can you reach?<\/p>\n\n\n\n

A) There is not sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90.<\/p>\n\n\n\n

B) There is sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90.<\/p>\n\n\n\n

C) There is not sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.<\/p>\n\n\n\n

D) There is sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.<\/p>\n\n\n\n

54) A major Blu-ray rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with Blu-ray players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have Blu-ray players. State the test of hypothesis that is of interest to the rental chain.<\/p>\n\n\n\n

A) H<\/em>0 : \u03c0 \u2264 0.32 versus H<\/em>1 : \u03c0 <\/em>> 0.32<\/p>\n\n\n\n

B) H<\/em>0 : \u03c0 \u2264 0.25 versus H<\/em>1 : \u03c0 <\/em>> 0.25<\/p>\n\n\n\n

C) H<\/em>0 : \u03c0 \u2264 5,000 versus H<\/em>1 : \u03c0 <\/em>> 5,000<\/p>\n\n\n\n

D) H<\/em>0 : \u03bc<\/em> \u2264 5,000 versus H<\/em>1 : \u03bc<\/em> <\/em>> 5,000<\/p>\n\n\n\n

55) A major Blu-ray rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with Blu-ray players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have Blu-ray players. The value of the test statistic in this problem is approximately equal to<\/p>\n\n\n\n

A) 2.80.<\/p>\n\n\n\n

B) 2.60.<\/p>\n\n\n\n

C) 1.94.<\/p>\n\n\n\n

D) 1.30.<\/p>\n\n\n\n

56) A major Blu-ray rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with Blu-ray players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have Blu-ray players. The p<\/em>-value associated with the test statistic in this problem is approximately equal to<\/p>\n\n\n\n

A) 0.0100.<\/p>\n\n\n\n

B) 0.0051.<\/p>\n\n\n\n

C) 0.0026.<\/p>\n\n\n\n

D) 0.0013.<\/p>\n\n\n\n

57) A major Blu-ray rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with Blu-ray players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have Blu-ray players. The decision on the hypothesis test using a 5% level of significance is<\/p>\n\n\n\n

A) to reject H<\/em>0 in favor of H<\/em>1.<\/p>\n\n\n\n

B) to accept H<\/em>0 in favor of H<\/em>1.<\/p>\n\n\n\n

C) to fail to reject H<\/em>0 in favor of H<\/em>1.<\/p>\n\n\n\n

D) We cannot tell what the decision should be from the information given.<\/p>\n\n\n\n

58) A major Blu-ray rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with Blu-ray players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have Blu-ray players. The rental chain&#39;s conclusion from the hypothesis test using a 5% level of significance is<\/p>\n\n\n\n

A) to open a new store.<\/p>\n\n\n\n

B) not to open a new store.<\/p>\n\n\n\n

C) to delay opening a new store until additional evidence is collected.<\/p>\n\n\n\n

D) We cannot tell what the decision should be from the information given.<\/p>\n\n\n\n

59) The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a side curtain air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the side curtain air bags. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30, which test would you use?<\/p>\n\n\n\n

A) Z<\/em> test of a population mean<\/p>\n\n\n\n

B) Z<\/em> test of a population proportion<\/p>\n\n\n\n

C) t<\/em> test of population mean<\/p>\n\n\n\n

D) t<\/em> test of a population proportion<\/p>\n\n\n\n

60) The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a knee airbag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the knee airbag. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30 and decided not to reject the null hypothesis, what conclusion could you reach?<\/p>\n\n\n\n

A) There is sufficient evidence that the proportion is 0.30.<\/p>\n\n\n\n

B) There is not sufficient evidence that the proportion is 0.30.<\/p>\n\n\n\n

C) There is sufficient evidence that the proportion is not 0.30.<\/p>\n\n\n\n

D<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

Answers<\/strong><\/h3>\n\n\n\n

51)<\/strong> The test statistic formula for a proportion is:
[
z = \\frac{\\hat{p} – p_0}{\\sqrt{\\frac{p_0(1 – p_0)}{n}}}
]
Given:<\/p>\n\n\n\n

    \n
  • (\\hat{p} = \\frac{83}{100} = 0.83)<\/li>\n\n\n\n
  • (p_0 = 0.90)<\/li>\n\n\n\n
  • (n = 100)<\/li>\n<\/ul>\n\n\n\n

    Substitute into the formula:
    [
    z = \\frac{0.83 – 0.90}{\\sqrt{\\frac{0.90 \\cdot 0.10}{100}}} = \\frac{-0.07}{\\sqrt{0.009}} = \\frac{-0.07}{0.0949} \\approx -0.737
    ]
    Answer: None of the options provided matches this exact value; verify choices.<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    52)<\/strong> Given (z = -2.20), compare with critical values at different (\\alpha) levels (one-tailed):<\/p>\n\n\n\n

      \n
    • At (\\alpha = 0.10, z_{crit} = -1.28): Reject (H_0).<\/li>\n\n\n\n
    • At (\\alpha = 0.05, z_{crit} = -1.645): Reject (H_0).<\/li>\n\n\n\n
    • At (\\alpha = 0.01, z_{crit} = -2.33): Fail to reject (H_0).<\/li>\n<\/ul>\n\n\n\n

      Answer: D) (a) yes; (b) yes; (c) no<\/strong><\/p>\n\n\n\n

      \n\n\n\n

      53)<\/strong> If the null hypothesis is rejected:<\/p>\n\n\n\n

        \n
      • Conclusion: There is sufficient evidence<\/strong> that the proportion of doctors recommending aspirin is less than 0.90<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        Answer: D)<\/strong><\/p>\n\n\n\n

        \n\n\n\n

        54)<\/strong> To test whether more than 5,000 households own Blu-ray players:
        [
        \\pi = \\frac{5000}{20000} = 0.25
        ]
        Hypotheses:
        [
        H_0: \\pi \\leq 0.25, \\quad H_1: \\pi > 0.25
        ]
        Answer: B)<\/strong><\/p>\n\n\n\n

        \n\n\n\n

        55)<\/strong> Test statistic for a proportion:
        [
        z = \\frac{\\hat{p} – \\pi}{\\sqrt{\\frac{\\pi(1 – \\pi)}{n}}}
        ]
        Given:<\/p>\n\n\n\n

          \n
        • (\\hat{p} = \\frac{96}{300} = 0.32)<\/li>\n\n\n\n
        • (\\pi = 0.25, n = 300)<\/li>\n<\/ul>\n\n\n\n

          Substitute:
          [
          z = \\frac{0.32 – 0.25}{\\sqrt{\\frac{0.25 \\cdot 0.75}{300}}} = \\frac{0.07}{\\sqrt{0.000625}} = \\frac{0.07}{0.025} = 2.80
          ]
          Answer: A)<\/strong><\/p>\n\n\n\n

          \n\n\n\n

          56)<\/strong> (z = 2.80). From standard normal tables:
          [
          p\\text{-value} = P(Z > 2.80) = 0.0026
          ]
          Answer: C)<\/strong><\/p>\n\n\n\n

          \n\n\n\n

          57)<\/strong> At (\\alpha = 0.05, z_{crit} = 1.645). Since (z = 2.80 > 1.645), reject (H_0).<\/p>\n\n\n\n

          Answer: A)<\/strong><\/p>\n\n\n\n

          \n\n\n\n

          58)<\/strong> Based on the rejection of (H_0), there is sufficient evidence to support that more than 5,000 households have Blu-ray players. The chain should open the store.<\/p>\n\n\n\n

          Answer: A)<\/strong><\/p>\n\n\n\n

          \n\n\n\n

          59)<\/strong> Testing a population proportion ((\\pi = 0.30)):<\/p>\n\n\n\n

            \n
          • Use Z test<\/strong> for population proportion.<\/li>\n<\/ul>\n\n\n\n

            Answer: B)<\/strong><\/p>\n\n\n\n

            \n\n\n\n

            60)<\/strong> Not rejecting (H_0) means there is insufficient evidence to conclude the proportion is different from 0.30.<\/p>\n\n\n\n

            Answer: B)<\/strong><\/p>\n\n\n\n

            \n\n\n\n

            Explanation (Question 60)<\/strong><\/h3>\n\n\n\n

            This is a hypothesis test for a population proportion, where:<\/p>\n\n\n\n

              \n
            • Null hypothesis: (H_0: \\pi = 0.30).<\/li>\n\n\n\n
            • Alternative hypothesis: (H_1: \\pi \\neq 0.30).<\/li>\n<\/ul>\n\n\n\n

              A sample of 200 compact-car owners indicates 79 would purchase the knee airbag, with (\\hat{p} = \\frac{79}{200} = 0.395). If the test fails to reject (H_0), it means the observed data does not provide strong enough evidence to conclude that the true proportion differs from 0.30. This could occur due to insufficient sample size, low statistical power, or the sample proportion being close to the hypothesized proportion.<\/p>\n\n\n\n

              Failing to reject (H_0) does not<\/strong> confirm that the proportion is exactly 0.30\u2014it merely means there isn\u2019t enough evidence to suggest otherwise. The decision implies retaining the status quo unless stronger evidence is available.<\/p>\n","protected":false},"excerpt":{"rendered":"

              51) A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-184390","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/184390","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=184390"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/184390\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=184390"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=184390"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=184390"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}