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According to a​ report, the mean of monthly cell phone bills was ​$48.89 three years ago. A researcher suspects that the mean of monthly cell phone bills is different from today. ​(a) Determine the null and alternative hypotheses. ​(b) Explain what it would mean to make a Type I error. ​(c) Explain what it would mean to make a Type II error. ​(a) State the hypotheses. Upper H 0​: ▼ mu p sigma ▼ greater than less than not equals equals ​$ nothing Upper H 1​: ▼ p mu sigma ▼ not equals less than equals greater than ​$ nothing ​(Type integers or decimals. Do not​ round.) ​(b) Explain what it would mean to make a Type I error. Choose the correct answer below. A. The sample evidence did not lead the researcher to believe the mean of the monthly cell phone bill is higher than ​$48.89​, when in fact the mean of the bill is higher than ​$48.89. B. The sample evidence led the researcher to believe the mean of the monthly cell phone bill is different from ​$48.89​, when in fact the mean of the bill is ​$48.89. C. The sample evidence did not lead the researcher to believe the mean of the monthly cell phone bill is different from ​$48.89​, when in fact the mean of the bill is different from ​$48.89. D. The sample evidence led the researcher to believe the mean of the monthly cell phone bill is higher than ​$48.89​, when in fact the mean of the bill is $ 48.89 . ​(c) Explain what it would mean to make a Type II error. Choose the correct answer below.

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Answer:

Step-by-step explanation:

a) The null hypothesis is the claim that is to be tested. Therefore, it is written as

H0 : μ = 48.89

The alternative hypothesis is the opposite of the null hypothesis. It is written as

Ha : μ ≠ 48.89

b) A type I error is committed when a true null hypothesis is rejected. To make a type I error, the correct option is

B. The sample evidence led the researcher to believe the mean of the monthly cell phone bill is different from ​$48.89​, when in fact the mean of the bill is ​$48.89.

c) A type II error is committed when a false null hypothesis is accepted. To make a type II error, the correct option is

The sample evidence did not lead the researcher to believe the mean of the monthly cell phone bill is different from ​$48.89​, when in fact the mean of the bill is different from ​$48.89.

Following are the responses to the given points:

  • The null hypothesis is indeed the assertion that will be tested.

                   [tex]\to H_0 :\mu = 48.89[/tex]

  • An alternate hypothesis is indeed the inverse of the null.

            [tex]\to H_a: \mu \neq 48.89[/tex]

  • Whenever a valid null hypothesis is false, a type I error is committed. The correct choice for making is a type I error.
  • This sample evidence forced the researcher to conclude that the mean monthly cell phone cost was less than [tex]\$48.89[/tex], whereas, in reality, the average bill is [tex]\$48.89[/tex].
  • Whenever a null hypothesis is false for accepting, a type II error is committed.
  • It making a type II error is the sampling data did not persuade the investigator to believe that the mean of the monthly cell phone bill is different from [tex]\$48.89[/tex] when in reality it is.

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