Question

Delmar claims that, on average, he practices the piano at least 2 hours per day. in a hypothesis test of this claim, h0 is µ ≥ 2 and ha is µ < 2, where µ is the number of hours, on average, delmar practices daily. the diagram shows the critical region for the hypothesis test. a normal distribution is shown. z = 1.65. the z-statistic for a sample of delmar’s practice times is 1.41. how should this statistic be interpreted in terms of the hypothesis test?

Answer 1

The z-statistic of 1.41 compared to the critical value of 1.65 indicates that we do not reject the null hypothesis, suggesting that Delmar practices piano at least 2 hours per day on average.

Step-by-step explanation:

The z-statistic for Delmar's practice times is 1.41, which must be compared to the critical z-value of 1.65. Since 1.41 is less than 1.65, Delmar's sample result falls outside the critical region. Therefore, we do not reject the null hypothesis (H0: μ ≥ 2), which claims that on average, he practices the piano at least 2 hours per day. To interpret the result of the hypothesis test given the z-statistic, in terms of Delmar's practice habits, the evidence is not sufficient to conclude that he practices less than 2 hours on average per day (which would support the alternative hypothesis Ha: μ < 2). Delmar's average practice time could indeed be at least 2 hours, or the sample may not have adequately captured a lower average if it exists.