Question

9. The display provided from technology available below results from using data for a smartphone​ carrier's data speeds at airports to test the claim that they are from a population having a mean less than 4.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

What are the null and alternative​ hypotheses?

A.Ho​: µ=4.00 Mbps

H1​: µ>4.00 Mbps

B: Ho​: µ=4.00 Mbps

H1​: µ≠4.00 Mbps

C: Ho​: µ=4.00 Mbps

H1​: µ<4.00 Mbps

D: Ho​: µ<4.00 Mbps

H1​: µ=4.00 Mbps

B.

Identify the test statistic.____

​(Round to two decimal places as​ needed.)

Identify the​ P-value.____

​(Round to three decimal places as​ needed.)

State the final conclusion that addresses the original claim.

(Reject, Fail to reject) Ho. There is (not sufficient, sufficient) evidence to support the claim that the sample is from a population with a mean less than 6.00 Mbps.

10. A simple random sample of 48 men from a normally distributed population results in a standard deviation of 8.1 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts​ (a) through​ (d) below.

a. Identify the null and alternative hypotheses. Choose the correct answer below.

a. Ho:σ≠10 beats per minute

H1: σ=10 beats per minute

B: Ho:σ=10 beats per minute

H1: σ<10 beats per minute

C: Ho:σ=10 beats per minute

H1: σ≠10 beats per minute

D: Ho:σ≥10 beats per minute

H1: σ<10 beats per minute

b. Compute the test statistic.

xˆ2=_____

​(Round to three decimal places as​ needed.)

c.Find the​ P-value.

​P-value=_____

​(Round to four decimal places as​ needed.)           

d. State the conclusion. (Do not reject, Reject) Ho​, because the​ P-value is (less than or equal to, greater than) the level of significance. There is (insufficient, sufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats per minute.

Answer 1

10)

C: Ho:σ=10 beats per minute

H1: σ≠10 beats per minute

b)

Ho :   σ =   10
Ha :   σ ╪   10
      
Level of Significance ,    α =    0.1
sample Std dev ,    s =    8.1
Sample Size ,   n =    48
      
Chi-Square Statistic,   X² = (n-1)s²/σ² =    30.837

degree of freedom,   DF=n-1 =    47
p-Value   =   0.0330

d)

Reject) Ho​, because the​ P-value is (less than) the level of significance. There is (, sufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats per minute.