IMathAS-libretexts

For users on Twitter, the number of followers has a skewed-right distribution, ranging from 0 to @justinbieber. As of 2016, the mean number of followers was 500. To see if academic mathematicians tend to have a typical number of followers, a study was conducted in which the Twitter accounts of 100 random academic mathematicians were analyzed to determine their number of followers. Within this sample, the mean was 484 and the standard deviation was 87. (The central limit theorem assures us that sample means of this size will be normally distributed.) Conduct the hypothesis test at the 5% significance level.

(a) The population mean being studied is:

μ = the mean number of Twitter followers among the 100 accounts sampled
μ = the mean number of Twitter followers among all users
μ = the mean number of Twitter followers among all academic mathematicians

(b) The hypotheses for the test are:

H₀: μ = 500
H_a: μ > 500
H₀: μ = 500
H_a: μ < 500
H₀: μ = 500
H_a: μ ≠ 500

(c) The test statistic is: (Please round to two decimal places.)

(d) The P-value for this hypothesis test is: (Please round to four decimal places.)

(e) Identify the conclusion for the hypothesis test. Recall that the significance level is α = 0.05.

Since the P-value is small, we reject the null hypothesis and accept the alternative.
Since the P-value is not small, we reject the null hypothesis and accept the alternative.
Since the P-value is not small, we accept the null hypothesis.
Since the P-value is not small, we do not have enough evidence to reject the null hypothesis.
Since the P-value is small, we fail to reject the null hypothesis.

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